When Steven Moffat leaves the series in 2017, the speculation is that the Scottish actor will depart at the same time - leaving new show runner Chris Chibnall to select his own Doctor.
The Mirror quoted an unnamed BBC source, who said: “Bosses are already discussing a fresh start when Steven leaves.
“They’ve been happy with what Peter has brought to the role but some think it might make sense to give Chris his own choice of actor to play the Doctor.
“They hope he will be able to find someone who can have the same impact as Matt Smith did when Steven Moffat kicked off his run as executive producer.”
This would follow a similar pattern as when Russell T Davies left with David Tennant in tow.
Here is a list of potential candidates who we think could replace Peter.
Robin Harper, former Green MSP
It’s not just the penchant for rainbow-coloured scarves or fedora - we reckon Robin Harper, the first Green parliamentarian in the UK, would be an excellent Doctor Who.
Admittedly more Tom Baker than Matt Smith, Harper - who along with his wife Jenny won the Golden Gavel award on Bargain Hunt in 2011 - would herald a return to a quirkier line of doctors.
Although perhaps the wrong type of Doctor for the new era of the programme which has seen the likes of 26-year-old whippersnapper Matt Smith, and the eternally youthful David Tennant, Harper could revamp the show with his green credentials. A hybrid Tardis, perhaps?
The 27-year-old Harry Potter star may have a baby face, but he is older than Matt Smith when he took over the part. Adding Grint into the series could even bring some younger viewers - after disappointing numbers at the premiere of series nine.
This British actor is best known for his roles in BBCs Luther and American series The Wire. Idris could bring a commanding presence to the Doctor on screen not seen in a few regenerations.
Unconfirmed reports speculate that Idris amy have been previously offered the role, but turned it down. He was also quoted as saying “I’d look stupid in a bow tie”, but we think Chris could help the actor bring his own sense of style to the 13th Doctor.
While the actor currently has his hands full with Steven Moffat’s other show - Sherlock - the recent Victorian flashback episode of that series has shown how good the actor might look in a tweed coat. While Ben was previously rumoured to be playing the Doctors arch nemesis, The Master, this was dismissed by the actor himself.
Many fans have long called out for a female Doctor, and Hayley might be just the person to play it. Best known for her role as Peggy Carter in Captain America and subsequently Marvel’s Agent Carter, she has shown that she can handle a world predominantly filled with men. The British actor has been outspoken about how more women need good characters instead of good female roles. Could Dr Who be one of those characters?
The Scottish actor is currently staring in ABCs Once Upon A Time, a fairy tale television series in America, but with a limited series surely he’d have enough time to take up the role of Doctor? His previous roles would make him an interesting choice for the more recently mild mannered regenerations of the Doctor we’ve become accustomed to, but it could be what the show needs to give it a proper fresh start.
Who do you think should be the 13th Doctor?