The actor, famous for his role as foul-mouthed Malcolm Tucker in The Thick of It, was down to 5/6 favourite with William Hill when they stopped taking bets.
Joe Crilly, a spokesman for the firm, said: “We have seen people today trying to back Peter Capaldi as much as possible at every price available and after a small gamble on Daniel Rigby overnight, it seems that Capaldi is once again in line to move into the Tardis.”
The identity of the latest star to play the time lord will be unveiled live on television this weekend amid tight security in a bid to prevent the identity leaking out.
Sources close to the show said only 10 people know the name of the new doctor, who will replace Matt Smith, and they are using the codename Houdini to try and keep it a secret.
Capaldi is a life-long fan of the show and even wrote a letter to the Radio Times about the Daleks when he was a teenager.
Plans for this Sunday’s half-hour show, which goes out at 7pm, were kept secret with a repeat of Celebrity Mastermind put in listings in its place.
The show will be presented by Zoe Ball and feature interviews with Smith and executive producer Steven Moffat as well as celebrity fans and some previous incarnations of the science-fiction hero.
Other names that were mentioned as possible contenders include Daniel Rigby, whose award-winning performance as Eric Morecambe in Eric and Ernie beat Smith to the best actor TV Bafta in 2011, and Cutting It star Ben Daniels.
Mr Moffat said: “The decision is made and the time has come to reveal who’s taking over the Tardis. For the last of the Time Lords, the clock is striking 12.”
BBC drama controller Ben Stephenson said: “We can’t wait to unveil the next Doctor with everyone live on BBC1 on Sunday night. Amongst all the speculation and betting, there has been lots of fun and intrigue at work as we’ve been using the codename Houdini as a decoy.
“It’s the biggest secret in showbiz, even those working with the new Doctor on other projects at the moment have no idea they are in the presence of the 12 incarnation.”
CONTENDERS FOR TIMELORD ROLE
The identity of the new Doctor Who will be revealed on Sunday.
Here are some of the leading contenders to take on the role of the timelord:
The Glasgow-born actor would be the first Oscar winner to take on the role if he was named as the new doctor.
He won an Academy Award in 1994 for the best short film (Live Action) for Franz Kafka’s It’s a Wonderful Life, but Capaldi really became a household name thanks to his performance as foul-mouthed spin-doctor Malcolm Tucker in The Thick of It.
He has also written several shows including a documentary about 500 years history of Scottish portrait painting and Cricklewood Greats - a spoof about the heyday of the British film industry.
The 30-year-old is probably most familiar to audiences for his role as Simon, the slightly feckless student in the BT adverts, but his talent is beyond question.
He won a Television Bafta for leading actor - beating Matt Smith in the process - for his performance as Eric Morecambe in the biopic Eric and Ernie.
The actor, who grew up in Stockport, also works as a stand-up and is due to perform at this year’s Edinburgh Festival.
The Cutting It star was installed as one of the early favourites when Matt Smith announced he was quitting and he has stayed near the top of the bookmaker’s lists ever since.
A career as an in-demand actor on stage and screen has seen appearances in Law and Order UK and House of Cards.
He is also due to join the next series of department store costume drama The Paradise to play former soldier Tom Weston.
The son of character actor Roy Kinnear has recently added the title of playwright to his lengthening CV.
His play, The Herd, is set around the 21st birthday party of a severely disabled man called Andy Griffith and includes Sherlock star Louise Brealey among the cast.
Kinnear, who has appeared in several Bond films and recently starred as Iago opposite Adrian Lester in Othello at the National Theatre, is also set to play Lord Lucan in a new series about the notorious aristocrat.
The Irish actor has had a critically acclaimed stage career, but it was his role as arch-villain Moriarty in BBC One’s Sherlock that made him a star.
The 36-year-old, whose career includes a blink and you’ll miss it part in Saving Private Ryan, made his first film appearance as a 17-year-old.
He is set to play a Soviet spy in a cold war thriller for BBC Two with Romola Garai and Simon Russell Beale.