It's obviously speculation, supposition and a whole mill of salt, but...
Doctor Who: Tilda Swinton is firm favourite to be the next Doctor | Metro News
Top ten odds:
Tilda Swinton – 7/2 (Favourite)
Kris Marshall – 4/1
Olivia Colman – 5/1
Maxine Peake – 8/1
Ben Whishaw – 10/1
Richard Ayoade – 10/1
Andrew Buchan – 10/1
Reece Shearsmith – 12/1
Phoebe Waller-Bridge – 12/1
Rory Kinnear – 16/1
Interesting that 4 out of the 10 are women