According to the Radio Times, the BBC has asked current Doctor Who star Peter Capaldi to stay on after Chris Chibnall takes over as show runner. When it was announced that Steve Moffat would be moving on the question of whether or not Capaldi would remain became the hot topic. It was speculated that Chibnall would want to start fresh with a new Doctor the same way Moffat had with Matt Smith.
But Capaldi is unsure if he will take the BBC up on the offer:
"I've been asked to stay on, but it's such a long time before I have to make that decision. Steven's been absolutely wonderful, so I love working with him. Chris is fantastic, and I think he's a hugely talented guy. I don't know where the show's gonna go then. I don't know. I have to make up my mind, and I haven't yet. As Steven will tell you, it's very difficult to say goodbye."
Personally, I hope he sticks around for at least a season with Chibnall as I'd love to see what the two of them would do together.