Gatwa, who is the new Doctor on the BBC1 sci-fi shows, starred alongside the Hollywood actor in the blockbuster film and said Gosling, who plays Ken, couldn’t wait to meet him.
“I remember Ryan Gosling bounding up to my trailer like, ‘Doctor Who is the coolest show in the world, man!" Gatwa told British Vogue.
“And I was like, ‘What the hell?’ This show has incredible reach.”
Gosling was previously snapped on the Barbie set wearing a T-shirt that featured Ncuti as the Time Lord.
In response, Doctor Who’s showrunner Russell T Davies, joked on Instagram that he would be suing the actor for wearing “illegal merch”.
Gosling also previously praised Gatwa for taking over the role that has been famously played by the likes of Jodie Whitaker and David Tennant.
He gushed to 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."
The news has sparked reports that Gosling, 43, who starred alongside Margot Robbie’s Barbie in the Box Office smash, has been approached for a guest appearance in the series, which returns later this year.
An insider told The Sun: “This would be a huge coup for the show, but also a real honour for Ryan who is something of a Whovian.
“It’s not clear yet what role he’d have, but the writers would tailor a character for him to play, if he could find the time in his packed schedule.”
Evening Standard has contacted representatives for the BBC and Ryan Gosling for comment.