The former Leeds boss is the new bookies' favourite, with Rotherham's manager being ruled out by the chairman.
Indeed, the 54-year-old is now priced at 1/1 to take over at Peterborough, which may have something to do with chairman Darragh MacAnthony's recent tweets.
The Posh chairman has ruled out moving for a number of candidates on Twitter, including Rotherham United boss Steve Evans.
Evans was the previous bookies' favourite but is now at 2/1, behind former Leeds boss McDermott.
Asked if he was considering Evans, MacAnthony responded to a fan on social media:
But former Leeds man McDermott was the only candidate to draw praise from the chairman on Twitter without a move being ruled out.
@DMAC102 Brian mcdermott? Would be a good appointment that darragh. Must be looking to get back into work now.— LUFC DAZZER (@darsum82) September 10, 2015
McDermott hasn't been in management since his Elland Road exit in 2014 but is a chief scout at Arsenal. A potential return at Peterborough would no doubt be welcomed by many who felt he was unfortunate at Leeds.