Comedian Richard Ayoade is said to be one of the names in the running to become the new Doctor Who.
Best known for his role in Channel 4 sitcom The IT Crowd, Richard was recently announced as the channel's new host of The Crystal Maze.
But the Beeb are reportedly keen to poach him away for the next series of Doctor Who in 2018.
"Richard is very highly thought of in the industry and is well liked," a source said. “Beeb bosses have discussed him as an option to replace Peter as they think he would bring something different to the role.
They explained to The Sun newspaper: “The final decision is still some way off and it’s all to play for.
"He’s very much seen as a Channel 4 poster boy so tempting him away would be something of a coup.”
Others tipped for the role include Phoebe Waller-Bridge and Kris Marshall.
The BBC declined to comment on the speculation.
This year's run is Peter Capaldi's last as the Doctor, previously announcing he would be stepping down at Christmas.
Capaldi first stepped into the TARDIS in 2013, and will leave the iconic role in the 2017 Christmas special after three incredible series of the BBC's global hit sci-fi drama.
Peter Capaldi said ahead of the current series kicking off: "One of the greatest privileges of being Doctor Who is to see the world at its best.
"From our brilliant crew and creative team working for the best broadcaster on the planet, to the viewers and fans whose endless creativity, generosity and inclusiveness points to a brighter future ahead. I can’t thank everyone enough. It’s been cosmic."
Peter Capaldi's final series also marks writer and executive producer Steven Moffat's last.
He said: "Like Peter, I’m facing up to leaving the best job I’ll ever have, but knowing I do so in the company of the best, and kindest and cleverest of men, makes the saddest of endings a little sweeter. But hey, it’s a long way from over.
"Peters’ amazing, fiery, turbulent Doctor is still fighting the good fight, and his greatest adventures are yet to come. Monsters of the universe, be on your guard - Capaldi’s not done with you yet!”