The Irish broadcaster has gone from being 33-1 to 14-1 to land the job after a surge in bets from fans, according to The Mirror.
Jeff Stelling announced his departure from the long-running Channel 4 series last week. The Sky Sports presenter admitted that he is "really, really sad" about finishing working with co-host Rachel Riley.
"The viewing figures are tumbling and Wogan could be just the man for the job," a William Hill spokesperson commented.
Gyles Brandreth and Aled Jones are still 6-1 joint favourites to replace Stelling, however.
A Channel 4 representative previously confirmed that the broadcaster is "already talking to a number of people" to take on the main presenting duties.
> Blackpool fan plays 'Countdown' prank