Capaldi, 55, who is better known for playing hot-headed Malcolm Tucker in The Thick of It, has been placed above Daniel Rigby, Ben Daniels and Rory Kinnear to play the next Doctor.
William Hills has 11/8 odds on Capaldi, making him the favourite to be handed the role, although Black Mirror actor Daniel Rigby has made a late entry into the top five seeing his odds slashed from 40/1 to 9/2.
Joe Crilly, a spokesman for William Hill, said: “Peter Capaldi remains the favourite as we await the announcement, but it does not appear that the result is as cut and dry as first thought with Daniel Rigby coming in for some late support.”
It is thought that Capaldi’s name began to surface after Doctor Who creator Steven Moffat said he would not rule out casting an older Doctor.
He said: “We’ve never not considered an older Doctor. It is completely on all the lists we make- there are absolutely older Doctors.”
Previous frontrunner Rory Kinnear has slipped to fourth place at the bookies after he revealed he had never seen an episode of the show.
Billie Piper, former Doctor’s assistant Rose Tyler, is the only woman listed by Paddy Power to take on the title role after it was rumoured earlier this week that an actress might be in the running.
But with odds on at 33/1 it doesn’t look like Piper will be emerging from the TARDIS on Sunday.
Odds to replace Matt Smith as the Doctor
Peter Capaldi: 11/8
Daniel Rigby: 9/2
Ben Daniels: 5/1
Rory Kinnear: 15/1
Andrew Scot 10/1