According to bookies William Hill, there has been a flurry of bets on Capaldi taking over from Matt Smith in the BBC sci-fi franchise at the end of the year.
Capaldi is known to be a huge Doctor Who fan and has actually already appeared in the show, starring as Caecilius in the story 'The Fires of Pompeii'.
Doctor Who showrunner Steven Moffat confirmed to Digital Spy at Comic-Con that casting a much older Doctor is very much a possibility.
"We've never not considered an older Doctor," he said. "It is completely on all the lists we make - there are absolutely older Doctors."
Other actors linked to the role over recent weeks include Rory Kinnear, Ben Daniels, David Harewood, Daniel Rigby and Damien Molony.
Watch Steven Moffat talking to Digital Spy about the 12th Doctor below: