And yet, as he sits calmly in the manager's office at The Dell, he gives the impression that a bomb could quite easily explode next to him and he would remain unruffled, speaking in a quiet, considered and measured tone, and so laidback that he makes Des Lynam look like hyperactive.
You mention that perhaps his image is very different from the person now in charge of Southampton since the start of the season. Souness agrees: "I've never been true to my image. I accept that I sometimes overstepped the mark, but I can tell you that, off the pitch, I've never been an overly aggressive person."
To prove his point, he tells you what he got up to during his self-imposed 18-month exile from the game after he walked out on Liverpool in 1993. "I know people won't believe me, but I spent nearly all my time in the garden, or playing with my two new puppies. Apart from actually playing football, I am at my most happiest with either my dogs, or planting in the garden."
The two puppies were bought after he learned that both his previous dogs had been shot while chasing sheep near his Cheshire home. He tells you this and looks genuinely sad. It was just one of a horrendous list of personal and professional problems that befell a man who, prior to 1991, had enjoyed nothing but the most stunning success in football.
At Liverpool he won everything there was to win, both domestically and internationally. He captained the greatest club in Europe, before making a lucrative move to Sampdoria. His step up to management, at the hitherto struggling Rangers, initiated the club's dominance in Scotland that has remained to this day. Not only did Souness revive the glory days at the great old club but, by signing first English stars and then, in Maurice Johnson, a Catholic player, he succeeded by taking the most enormous and brave risks.
This, though, was not enough. When Liverpool came in for him after Kenny Dalglish's sudden departure in 1991, Souness leapt at the chance to return to Anfield. He was not to know at the time, of course, but his life would dramatically change.
"I was not satisfied at Rangers, not by a long way," he recalls. "I have hassles there, I had obstacles placed in front of me, and certain things never sat easily on my shoulders, and never will." Such as? "Well, I'll never be comfortable with bigotry, and it will always be at Rangers."
The Liverpool move seemed like the dream appointment, both for the club, and for Souness. It quickly became obvious that his time there would be anything but smooth. "Looking back I was blinded by my feelings for the club," he admits, talking slowly, and making every word count. "I've never allowed this to happen since.
"Bill Shankly had a problem telling players like St John and Yeats that they were too old and, as a result, he went seven years without winning anything. He'd got too close to some of the players, but he never made that mistake again.
"As a result Liverpool became the best, because they never allowed sentiment to come into their decision-making. They always outed you at the first sign of decline. Then they'd give a new player a season or so to look at the scene before moving into the first team. I can tell you that when I was the manager there, I never enjoyed such a luxury."
Why? He pauses for a second, deep in thought, before delivering his answer. "I've never said this before, but Kenny had been through Heysel and Hillsborough with some of his players. He'd become so emotionally involved with the whole Liverpool thing that he found it hard to say 'thanks, but no thanks'. Then I came along, and my job was to move all these people away. So I was the bad guy. Nobody's ever written or said that.
"Sure, I know I made mistakes, in both my manner, and the way in which I tried to change things too quickly. But everyone accepted when I took the job that it was the most difficult period for the club in its recent history. We managed to win the Cup in my two and a half years, but my timing was all wrong. Players like Redknapp, McManaman and Fowler were waiting to flourish, but were still too young. Now look at them."
His problems at work were nothing compared with his problems at home. Souness faced not only a bitter divorce, and the death of his father, but the sudden news that he required urgent open-heart surgery.
"I was fit when I walked into hospital, and fit when I walked out again. I was asking myself why I was in there in the first place. It was only when I became infected, 10 days later, that I was scared. That nearly killed me, and the memory has stuck."
A triple by-pass operation for a then 38-year-old man would scare most people, but he insists he took it all in his stride. "I told the hospital staff I would be their best ever patient. It was a shock, and if I had to go through it again I'd be scared, but the only time the whole mortality thing hit me was when, while recovering from the infection, I had a panic attack.
"I used to slip out of the back to avoid the press and go for a walk with a nurse. One day, when they decided I was safe to go out unaided, I walked in some woods nearby. I remember going off the track and trying to return a different way. I came to a fence and that's when the panic set in. The thought of collapsing, or falling over there, in the woods, kept flashing through my mind."
He returned to Liverpool, but by then the rot had set in. Results proved erratic, and mutterings of discontent from within the club became public knowledge. "From the operation, until the day I resigned in April, 1994, I didn't enjoy the job."
What particularly hurt this proud man was how players, past and present, turned on him. "The criticism I received from some of the people I played with really pissed me off," he admits. "I think of them as professional Scousers, people who went on and on about their love for the club. Nobody could accuse me of not putting everything into Liverpool, both as a player and as a manager.
"The players who turned against me were the same ones whose battles I used to fight when I was playing with them. Liverpool always used to expect the older, more experienced players to put things right if things weren't going well. I adopted the same approach, but players like Steve Nicol, Bruce Grobbelaar and Ronnie Whelan were all queueing for their testimonials.
"Contrary to popular belief I was under no pressure, but I'd fallen out of love with football. The chairman suggested I should give it a little longer at the club, but I told him I didn't enjoy it any more."
What did you feel as you drove away from his house? "An enormous sense of relief."
By now the transformation of Graeme Souness was well under way. This began the day he met Karen, who would become his second wife. "As a younger man I had only ever seen things my way," he now accepts. "I enjoyed success using these methods, but doing it my way, and the standards I set myself, made me ultimately ill. What happened with my heart would have happened anyway, but my ways of handling things brought the operation forward by 10 years.
"The problem was I was never satisfied with my lot. I always felt that I could do more. And I wasn't prepared to listen to others. The passion and the pride, and the goals I set myself meant that I was never content with life. Karen's taught me to listen to others. In fact, I've learned a hell of a lot in the past five years, and the funny thing is, despite all the traumas, I've never been happier.
"As my doctor explained you get two types of people: type A and type B. Type B would find my life extremely stressful, and would find sitting at home with his pipe and slippers to be relaxing. Type A would find sitting at home stressful, and football management relaxing. That's me. Nobody's ever advised me to stop doing what I do."
A Turkish cup win did not prevent Souness from falling foul of a new club board who preferred to employ the national coach instead of the Scot, but at least he left the country with fond memories, no bitterness, and one memorable moment when the old Graeme Souness reared its head and planted the Galatasaray flag in the centre of Fenerbahce's pitch following the cup win over their city rivals.
"The Fenerbahce vice-president had made some smart-arse comments about me being a cripple earlier in the season, and it was just a spontaneous action," Souness explains.
Did anyone at Galatasaray mind?
"No way. I got the biggest kiss of my life from the president."
Having recently made Dave Merrington's services surplus to requirements, Southampton then decided to approach the now available Souness, a clear statement of intent from the hitherto sleepy South Coast club.
"A friend of Lawrie McMenemy's sounded me out," he explains. "My enthusiasm for the game was right back and I fancied a chance to pit my wits again in the Premiership, and with a club who, by the very nature of their size and prospects, presented a new challenge for me.
"I came down and had a chat with Lawrie, who has been a friend of mine for many years now. As a result, we soon reached an agreement, and here I am. My aim is to ensure that when Southampton get their new stadium, in a couple of years' time, we are not only still in the Premiership, but have improved sufficiently to be able to immediately move into the next tier which has developed in the League, boosted by 30,000 fans. We may not become a super club, but there's no reason why we can't emulate what Middlesbrough have achieved."
One win in their first nine Premiership outings up to yesterday's draw against Coventry - which left them third from bottom - suggests the season will be long and hard, but not to the relaxed Souness.
"I'm actually more optimistic now than I was at the start of the season," he reveals. "I'm encouraged by the way we've played, and by the response I've had from the players. We've more than held our own in most games, and I'm a great believer that luck always evens itself out over the course of the season. I don't expect to be third from bottom of the League for too long."
Even if he is, the new, unfazed Souness will take it in his stride. "I couldn't be happier. My life is full: I'm a better football coach, and a better person for everything that's happened to me. I didn't set out to alter, but circumstances have definitely changed me.
"I now know that in two years' time I might be a successful manager here at Southampton, or I could be in the garden planting shrubs. Whatever happens will happen, that's the rollercoaster of life. What matters is how you handle the slumps."
If anyone should know the answer to that question, it is Graeme Souness.