"Everyone wants some of his time at the moment and I have to make sure he doesn't think he can just stop working," he said. He needn't have worried. Gunnlaugsson is as level- headed as they come and says he owes everything to Todd. "He took a gamble on me when I was fed up with football and I will never forget that."
With 12 goals in 15 games, Bolton's Icelandic international is proving a handful for First Division defenders, as Sunderland will find when they visit the Reebok Stadium today.
It wasn't always like that. When he arrived in England a couple of summers ago, Gunnlaugsson had just got over a series of injuries to his hamstring and Achilles tendon. He was, as he says, fed up with football and constantly trying to get himself fit.
Throughout most of last season, he watched in frustration as his team- mates, including his compatriot Gudni Bergsson, battled for their Premiership lives. He made only a handful of starts and when the new season began in August, he found himself still on the bench back in the Nationwide League. Then everything changed. "I came on as a late sub in our first game against Crystal Palace and scored. It was such a relief. I haven't looked back since. I always knew I had the talent."
So did his manager, who persevered with Gunnlaugsson because he could see the potential. "It's true he did not come up to expectations early on," Todd said. "He wasn't doing enough to hurt opponents in the box. He wanted to work too much from midfield. He just took time to adjust to how I wanted him to play."
During the close season, Todd noticed a difference. "He came back after the summer with such a strong desire, as if he felt he had something to prove. He has great balance and excellent pace. In the area, you can't get near him."
A free transfer under the Bosman ruling, Todd has clearly found himself a bargain, and a widely travelled one at that. Although still only 25, Gunnlaugsson, who is naturally left-footed, has played for Feyenoord, Nuremberg in Germany, Sochaux of France and, either side of all three, his home-town team, Akranes, Iceland's leading club just outside Reykjavik. "He's pretty streetwise," said Todd.
Gunnlaugsson's twin brother, from whom he was inseparable earlier in his career, plays for Brann Bergen in Norway and has flown over to watch this afternoon. "We signed for every club together before he went to Norway and I came to England," said Arnar. When his brother goes home tomorrow, Gunnlaugsson will still enjoy strong Icelandic links in Lancashire, whether at home with his girlfriend or on the field with Bergsson, the former Tottenham defender.
"Gudni was like a father figure for me last season when I was out of the team," said Gunnlaugsson. "I kept asking him what was wrong. He was a shoulder to cry on."
Life has changed since then, at international as well as club level. Iceland, for whom he has 25 caps, are upsetting the established order in Europe having already drawn with France and beaten Russia in their qualifying group for Euro 2000. "We can only play for four months of the season back home and to be honest we don't play the most attractive football. But we are solid and committed and for a country the size of ours (270,000) to do what we've done so far is quite an achievement."
So impressed is Todd with his latest goalscoring sensation that he has just imported a third Icelandic player, Eidur Gudjohnsen, who played with Ronaldo at PSV Eindhoven. Out of the game for 18 months with a broken ankle before Todd snapped him up, Gudjohnsen, still only 20, has just got injured again and not yet appeared in the first team.
When he eventually does, Bolton could have unearthed another jewel from a country more famous for its geysers, waterfalls and earthquakes.