Radio Times has this to say:
The new Doctor could be handed the keys to the TARDIS as early as next month, BBC sources have confirmed - with insiders suggesting Matt Smith’s replacement needs to be announced before the Doctor Who Christmas special begins filming next month.
The Twelfth Doctor is expected to first appear on screen at the end of the Christmas special, following the regeneration of Matt Smith’s Doctor.
It would be virtually impossible to keep the identity of the new doctor a secret even if the entire set went into lockdown during filming of the Christmas special, a BBC source told RadioTimes.com.
“The search has begun in earnest and is active now,” the source said, adding that the BBC has not ruled out hiring a woman to replace Matt Smith.
The decision will be made by a small team of BBC executives and kept under wraps. It will be decided by showrunner Steven Moffat, Danny Cohen, the BBC’s new head of television, controller of drama commissioning Ben Stephenson, casting director Andy Pryor and the show’s incoming executive producer Brian Minchin.
The new series, expected to be 12 episodes long, begins filming in the autumn.
A special marking the show’s fiftieth anniversary on 23 November 2013 has already been shot.
Smith announced this weekend that he is to leave the show at the end of this year after four years playing the Time Lord.
The 30-year-old actor said working on the show had been "the most brilliant experience".
Smith, who took over from David Tennant, was the youngest actor to play the role.
A BBC source also moved to squash speculation that showrunner Steven Moffat could also be calling it a day, insisting that he has signed up for at least another year.
In his statement on Smith’s departure, Moffat said: "Great actors always know when it's time for the curtain call, so this Christmas prepare for your hearts to break as we say goodbye to number 11. Thank you Matt - bow ties were never cooler."
Whoever takes the role, one actor considered to be one of the favourites in the early betting has already ruled himself out. Episodes and Green Wing star Stephen Mangan tweeted: “I see I’m 14/1 to be the new Doctor. Don’t waste your money.”