The former BBC One series moves over next year but it's already been confirmed that current presenters Mel and Sue won't be following.
According to the Daily Mirror newspaper Davina - who as well as BB has hosted The Million Pound Drop and The Jump on Channel 4 - is "top of bosses’ wish list" along with Clare Balding.
Strictly presenter Claudia Winkleman is also linked to the role although this looks unlikely due to her BBC commitments.
Another rumour is presenter Anna Richardson, but that could be rather awkward with her dating former co-host Sue Perkins.
As for the judges when Bake Off moves to Channel 4, Paul Hollywood and Mary Berry's future remains uncertain.
The pair haven't yet declared their intentions but Paul has hinted he may at least stay with the show as it moves.
However if Paul does go, a replacement may already be waiting in the wings.
Channel 4 regular Jamie Oliver is one of the names that could join and he told the Daily Star newspaper today: "The whole family loves it. Secretly there’s always a part of me in mourning because I’d love to be one of the judges.”
Celebrity chef Simon Rimmer has also been tipped for a potential role, depending if Mary and Paul decide to sign up to Channel 4.
For now, the Great British Bake Off continues its final BBC One series on Wednesday nights at 8PM.