Manford, who only began presenting the show in July alongside Alex Jones, quit the magazine show with what is believed to be immediate effect last night, following more revelations about his private life.
Paddy Power has now placed Baker as the 3-1 favourite to land the role from Monday to Thursday.
However, the Countryfile presenter's commitments to Strictly Come Dancing and next year's tour could prevent him from taking the job.
The bookmaker has put former host Adrian Chiles at 16-1 for a shock return from ITV, where he currently hosts Daybreak and the network's football coverage.
According to reports guest presenters will fill in until a permanent choice is made.
> Jason Manford deletes Twitter account