The project, which has a working title of No Strings Attached, would be hosted by a puppet and air on Saturday evenings.
The series would see the puppet interviewing celebrities in a "quite cheeky and brash" way, Broadcast reports.
The host could be based on a real person and the show is also expected to include sketches and games with a number of different characters.
The Jim Henson Company, the team behind The Muppets, is involved and Henson's son Brian Henson has had talks with the BBC's executive editor for entertainment Karl Warner.
"It's a really early doors development, but we have high hopes," Warner said. "The idea is that it will be very firmly anchored in the world of the chat show, but based around a new character created by the Henson Company.
"The Muppets were a massive phenomenon and nobody seems to have been developing anything in this area for a long time. The Henson Company has shown us some puppets, and their versatility is very exciting, but we are still only in talks at the moment."
The Muppets have been in the news lately, following the success of the latest movie. Yesterday, it emerged that a sequel is currently in the works.
Watch the trailer for the Muppets movie below: