Suddenly his eyes went misty and he departed into his mind's eye for a moment, sunny Euro 96 highlights on replay. The moment was given added piquancy by the knowledge that we were meeting at the very time Terry Venables was being confirmed elsewhere in London as Australia's new coach.
Sheringham has been inextricably linked with Venables for the last five years, signed by the then Spurs chief executive from Brian Clough and Nottingham Forest in a pounds 2.2m deal that we are led to believe - though see no evidence - is still being investigated by the Premier League's bungs inquiry. And of course there was the summer of '96 when Venables's belief in Sheringham was vindicated by a series of performances that see him, or should do, as the natural partner for Alan Shearer in the England team.
Now the what-might-have-been of the Venables era is gone, and Sheringham contemplates coldly the modern Spurs and their derby against Arsenal at Highbury today, always one of the purest in the English game, in locality and rivalry if not in nature. It will be conducted against a backdrop of the changing profiles of the two clubs. Arsenal have become the passing team, adding more sophistication to their game first under Bruce Rioch, now Arsene Wenger. Post Venables, an era that Sheringham says has "always been stop-start", Tottenham have followed the doomed abandon of Ossie Ardiles with the functional organisation of Gerry Francis.
It has made Spurs, in the game's parlance that damns with faint praise, difficult to beat, and is a triumph for Francis's coaching amid the fiscal restraints imposed by the chairman Alan Sugar, who refuses to join the clamour for expensive foreign talent after his sour experience with Jurgen Klinsmann. It is significant that Francis, needing a new striker to augment the squad, has turned to safe, solid old Norway to sign Steffen Iversen from Rosenborg of Trondheim for pounds 2.5m.
Indeed, the mediocrity that early season brought led Tottenham's most gifted and celebrated of strikers, Jimmy Greaves, to label them "Wimbledon with fans". Sheringham, now the Spurs captain, pauses to consider his words when the criticism is put to him. He does not dismiss it out of hand.
"Yeah, it's not good is it?" he replied. "It hurts that we are not in for the quality players, ones who are proven winners." A gap has consequently grown, he agreed, between the dynamism at the top of the Premiership and clubs clinging on to notions of their size and status based on reputation but in danger of being left simply to seek comfort from cups. It is now 35 years since the Double.
"It's very difficult," he said. "Tottenham has always been my club. I really want to succeed here. It's the tradition, the support, the whole ground with its pictures on the walls of great players and great games. Even when I was with Millwall and Forest, I always had this hope that one day I might play for them.
"Spurs have always had the image of being flamboyant but a winning club as well. I've always seen them as the biggest club in London. They have that class, that style to suit my philosophy on football. I know Arsenal have won a lot of things but it seems to me they are the dour ones. Spurs are the flashy ones, Arsenal the workmanlike ones."
He is ready with the answer when you turn Gunners' advocate. "I want to win things as well, which is what I envy about Arsenal, but I also want to win them in style. I remember years ago joining up with England and Paul Merson would have a go at the way we played. `Yeah, but you are boring', I'd say and he would just tell me to look at his medals."
Spurs, you reassure Sheringham, have always been known as the club who buy centre-forwards while Arsenal collect centre-halves and some of his own concerns now emerge, no matter how diplomatically expressed. "It's not really been that way, has it?" he replied. "We have got the tradition but we haven't produced have we?"
"Gerry was the ideal man and he has sorted out the foundations," he said. "We have got the stability, now it's making the next step." And how do Spurs do that, to re-stablish themselves among the elite? "It's difficult for me to say. I can only play to the best of my ability. I can't tell people who run the club what they are going to do because they have already made it clear what they are going to do. They have their own philosophies."
You ask him if the need is fundamentally for more flair to gild the solidity and he pauses again. "I think having Darren Anderton back will make a big difference," he said. "I know you shouldn't rely on one player but he starts things moving for us. He gives me the ball where I want it and how I want it. He is class but a winner as well and that's what you should have if you want to play for this club."
The reservations are clear, if understated. "We have got some outstanding players at the club - look at the England squad men we have," he says. "We are never going to struggle but if you want to win things you have got to do a little bit more. We need that desire to win and that comes from within."
It sends him gazing wistfully a few miles south again. "Arsenal have it, with their background and foundation. People say they need two new full-backs, that the defence is getting old, but they are sorted out as a unit. From there, they can go forward and produce. I love Tony Adams as a player and I like the look of Patrick Vieira. David Platt brings the experience, Dennis Bergkamp gives them class and Ian Wright is always going to score goals. I'm sure they will finish in the top three this season."
It may sound pessimistic but Sheringham has never been known to be that. He has retained a firm belief in his own worth when all except managers with a keen eye for a player doubted him. Under George Graham at Millwall, he admits to being a know-it-all until John Docherty told him similar things - work at defending from the front, don't just go for the spectacular goal - and the penny dropped.
The result, after a strange spell with Clough when he says he received little coaching, is a player who has matured into a canny and composed striker whose now appreciated reputation has moved beyond those perhaps with more leg power but certainly less brain power. Tottenham have come to rely on him, possibly too much.
To Sheringham, with Anderton in tandem, will fall the task today of picking a way through Arsenal's three centre-backs while at the other end the prospect of the developing Sol Campbell dealing with Bergkamp and Wright is intriguing. Last season's equivalent fixture finished goalless, a result which should not be repeated.
Arsenal, indeed, have struggled against Spurs since the Venables era - winning only one of eight Premiership confrontations - when he made it a priority that Tottenham would no longer be "outstrengthed" in these derbies.
In theory, Sheringham said, this should be the season Tottenham take off after Francis's establishing of consistency. With summer optimism a memory, cold North London practice should tell us whether that can become reality.Reuse content