The BBC declined to comment when contacted by RadioTimes.com.
Rumours of Gosling joining the cast have swirled for some time, with returning showrunner Russell T Davies playing them down during an appearance on The One Show last year.
He told host Jermaine Jenas at the time: "Let me tell you, Jermaine, you're a beautiful man, but if Ryan Gosling was in Doctor Who, I wouldn't be sitting here. I would be in Cardiff with my good mate Ryan, having a drink."
However, Gosling has made no secret of being a huge Doctor Who fan, well and truly breaking the internet when he donned a shirt with a fan-made design of Gatwa as the Doctor as news of his casting was first announced.
Gatwa later revealed that the pair had chatted about the show on the set of Barbie (as you do) after he was confirmed as the new Doctor.
He recalled to British Vogue earlier this year: "I remember Ryan Gosling bounding up to my trailer like, 'Doctor Who is the coolest show in the world, man!' And I was like, 'What the hell?' This show has incredible reach."
Gosling also told The One Show: "I am such a big fan of Ncuti's, he's the coolest, and him playing Doctor Who is like the most exciting thing that's happening right now. I'm here for it."
Doctor Who is no stranger to a famous guest star or two, with the likes of Kylie Minogue, Andrew Garfield, Bill Nighy, Carey Mulligan, and James Corden among those to have featured on the show.
Recent reports have also suggested that Davina McCall will feature in the Christmas special, with the BBC also declining to comment.
David Tennant and Catherine Tate are set to star in three anniversary specials this November, with Gatwa then taking over the keys to the TARDIS alongside Millie Gibson.
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