Strachan’s side are second in Group D as they prepare to face the Republic of Ireland at the Aviva Stadium on Saturday in a crucial clash.
Victory for the Irish would see them leapfrog Scotland in the group standings but they will take on a resurgent side that has won three out of five European Qualifiers to date.
Former Celtic and Southampton boss Strachan’s contract expires in November, a month after Scotland are due to complete their qualification bid, but Regan is keen to retain the 58-year-old’s services for an extended period.
“Gordon Strachan has probably done as much as (SNP leader) Nicola Sturgeon to rally the nation right now,” said Regan.
“We’ve had a laugh and a joke about his popularity amongst Scotland fans.
“As far as we are concerned if he keeps winning matches he can have a job here until he collects his bus pass.
“He’s doing a great job but it’s too early to go into any details. We are focusing on qualification right now.
“We would like to qualify. Gordon is quite relaxed about (his contract situation). We’ve had discussions and we will have a conversation at an appropriate time down the line.”
Regan feels there is a positive mood in the camp ahead of their “massive game” with Ireland and admitted he is pleased with the extent to which Strachan has improved the team’s fortunes.
“It’s a huge week for Scottish football, probably the biggest week in my time as chief executive,” added Regan.
“It’s a massive game and we have not been as close to qualification as this for some time.
“The way that Gordon has got the team playing now, we are full of optimism and full of hope. Everyone wants to be part of the squad and even for the friendly we had the other night (a 1-0 win over Qatar) there was a full turn-out of players wanting to take part.
“It’s really encouraging. I think we have a great chance. It will be a tight game, a very intense game but one we hope we can get a result from.”
Watch Republic of Ireland v Scotland on Saturday. Coverage begins on Sky Sports 1 and Sky Sports 5 from 4pm.