Despite Forest impressing in their comfortable 4-2 home victory over Leeds on Boxing Day, O'Driscoll was relieved of his duties shortly after the game, leaving the club sitting just a point off the play-offs.
McLeish was installed as a 20/1 outsider for the post with Roy Keane (now 14/1) the early favourite, but heads the betting at 1/4 after attracting the majority of the early money.
Hughes, meanwhile, has emerged as the 5/4 favourite to become the next Blackburn boss after Henning Berg was surprisingly sacked on Thursday morning.
Sky Bet Football Trader Chris Spicer said: "Keane is the man that has been widely tipped to succeed O'Driscoll but all the early money has been for McLeish, with Roberto Di Matteo (8/1) also attracting a fair bit of interest.
"It appears that the Forest owners want a quick appointment but it is hard to decipher exactly how much capital they are willing to commit.
"Hughes is the only name that people are going for at the moment in the next Blackburn manager market - he has been subject to over 90 per cent of bets so far and appears to be the fans' choice as well."