Alex McLeish: I'd take the Sunderland job in a shot if I was offered it
McInnes, currently on holiday, has been the leading contender to replace David Moyes at the Stadium of Light despite a flurry of bets on Manchester United legend Ryan Giggs on Wednesday.
Giggs remains the bookies favourite but his odds have drifted and the Gazette understands there has been no contact yet between the Black Cats and Giggs.
Chief executive Martin Bain is stepping up the search for a new manager this week and is expected to meet some of the prominent candidates.
The Scot is known to favour experience of the Championship, given the scale of the rebuilding job required at Sunderland, hence why the likes of McInnes, Paul Lambert and Paul Heckingbottom have been mentioned.
And McLeish says the chance to take on one of the "big jobs" in England doesn't come round too often.
Ex-Rangers, Scotland and Birmingham City boss McLeish told the Evening Express: "I would go to Sunderland in a shot if I was offered the job.
"Derek has done a great job at Aberdeen but the opportunity to take one of the big jobs in England doesn’t come along too often.
"And Sunderland is a big job."
Giggs himself is minded to wait for an opportunity to manage in the Premier League, narrowly missing out on the Swansea City job last year when the club opted for Bob Bradley instead.
He was the firm early favourite to replace Steve Agnew at Middlesbrough, but Garry Monk and Nigel Pearson look to be in pole position to compete for that role.
Sunderland have been determined to take their time in replacing Moyes in order to find the right candidate, with a large number of candidates interest in the role.