The broadcaster is currently working with The Jim Henson Company on a brand new Muppets-style entertainment show, reports BBC News.
The show's working title is No Strings Attached, and will feature puppets interacting with celebrity guests.
Baker tweeted: "I'm writing the new Muppet/Puppet show for BBC/Henson. There I've said it."
The BBC Radio 5 Live and BBC London presenter also posted a photo of himself holding up a Kermit the Frog cuddly toy.
A BBC spokesperson confirmed back in March that the channel was developing a new chat show format hosted by a new puppet character.
The show was then looking for "a warm, funny, cheeky, Saturday night host".
Stephen Fry had previously fronted a pilot of a Muppets-style show, but it was never broadcast.
The BBC axed its comedy puppet series Mongrels after two series in January.