The Northern Ireland boss held talks with Scottish football’s governing body last week after a compensation package was agreed with the Irish Football Association (IFA).
However, O’Neill turned down the approach, saying in a statement that he didn’t feel it was the ‘right opportunity’ for him at this stage in his managerial career.
But while SFA chief executive Stewart Regan has been forced to return to the drawing board - or at the very least, the remaining candidates on his shortlist - McLeish has offered his services.
The former Rangers manager told The Herald: “The Scotland job still interests me. I know that Michael O’Neill was the favourite but it wouldn’t be the first time I’ve got a job on the rebound.
“When I went to Hibs, for instance, Rod Petrie fancied Paul Sturrock and the rest is history.
“But if it’s meant to be, it’s meant to be. I’m more than open to the possibility, so we will see.”
McLeish took charge of Scotland for ten games in 2007, winning seven and losing three, before taking the vacant managerial role at Birmingham City.
In post for less than a year, McLeish led Scotland to victory over France in the Parc des Princes and posted a 70 per cent win rate - the highest of any Scotland manager who took charge of ten games or more.
However, defeat to Georgia in Tbilisi and a controversial loss to Italy at Hampden scuppered Scotland’s chances of making it to Euro 2008.
But McLeish believes his experience from his first spell, along with spells in club football with Birmingham, Aston Villa, Nottingham Forest, Genk and Zamalek, will stand him in good stead.
“Managers like myself, Walter Smith, we know what it’s all about in terms of experience,” McLeish continued.