TV
The bookmaker is offering odds of 3-1 on the Harry Potter actor taking over from David Tennant. Other favourites include James Nesbitt at 5-1, Damian Lewis at 6-1 and, at 8-1, Rhys Ifans.
Radcliffe, currently 18, would be the youngest ever Doctor. But a source commented: "Daniel would be fantastic. It is very early days but everyone can imagine him in the role.
"He would add a new dimension for all the young fans."
Programme maker BBC Wales declined to comment.
It has been rumoured that current actor Tennant may leave the role for good in two years' time. However, he has recently committed to the whole of the next series, airing from next year, plus three specials, due to air in 2009.
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