The former ‘Death In Paradise’ star is reportedly being lined up to play one of the Doctor’s assistants when the BBC show returns next year.
The 44-year-old actor had been an early favourite to replace Peter Capaldi, who quit his role as the twelfth Time Lord in January.
A source told the Sun: “Kris is a big fan of the show and the BBC are a big fan of his.”
It is thought Kris would replace Pearl Mackie as the Doctor’s assistant, who is rumoured to be stepping down after one series, whilst former ‘Little Britain’ star, Matt Lucas, will remain as a second assistant.
Kris announced he was leaving ‘Death In Paradise’ in February, after playing Detective Inspector Humphrey Goodman for four series.
A BBC spokeswoman told HuffPost UK there had been no decisions yet on companion casting.
On Sunday, the BBC confirmed that ‘Broadchurch’ star Jodie Whittaker would be replacing Peter Capaldi when he leaves the show following the 2017 Christmas episode.
Jodie was unveiled as the thirteenth Doctor in a teaser trailer, which premiered after the 2017 Wimbledon Men’s final.
Speaking about her major new role, Jodie said: “I’m beyond excited to begin this epic journey – with Chris and with every Whovian on this planet.
“It’s more than an honour to play the Doctor. It means remembering everyone I used to be, while stepping forward to embrace everything the Doctor stands for: hope. I can’t wait.”