On Sunday the Sun said Alexander was thrashing out final details with the BBC to succeed Jodie Whittaker and become the 14th Doctor.
If it happens, Alexander, 30, would be the first out gay actor to play the Time Lord.
Whittaker’s departure from Doctor Who has not been announced, although rumours abound that the next series and two special episodes, to be broadcast next year, will be her final outings.
Whittaker joined the show in 2017, regenerating from Peter Capaldi to become the first woman to play the Doctor.
On Sunday, the BBC said it had no official comment on the matter. It released a statement attributed to a BBC insider which said: “As ever bosses are staying tight-lipped about what they have planned but, with filming still going on, they clearly have plans for episodes to be playing out much later into 2022 so there’s lots more to come for Jodie’s Doctor.”
According to reports, Alexander is being supported by Davies, who revived the franchise in 2005 after a 16-year hiatus. He was the showrunner for the series that starred Christopher Eccleston and David Tennant as the Doctor.
Alexander was best known as the frontman of Years & Years before proving himself as an actor of considerable talent in Davies’ recent Channel 4 drama, It’s a Sin. For some, he also stole the show at this year’s Brit Awards with a duet with Elton John.
Speculation as to who the next Doctor will be is up there with who the next James Bond will be. Names which have recently come up, for the Doctor, include Phoebe Waller-Bridge, Michaela Coel, Richard Ayoade, Kelly Macdonald, Jodie Comer and Tom Rosenthal.
The casting of Alexander would not be a surprise, but the rumour might also be wide of the mark given the high levels of secrecy around the show.
“The hardest secret to keep was my own!” she said. “That was a really long time in my life – the gap between auditioning to play the Doctor, being given it, and it being announced.
“Professionally, I was the only person in my team that knew I’d been cast. I’d be sent auditions and I’d go [faux diva voice] ‘I’m really sorry, I don’t really want to put myself up for that.’”
Back in 2017, some newspapers reported that the next Doctor would definitely be Waller-Bridge. Others said it would be Kris Marshall. It was neither – meaning it might not be Alexander.