The Sex Education star, whose role in Doctor Who was announced in May, has recently been filming the forthcoming Barbie film with La La Land actor Gosling.
On Sunday (26 June), Gosling was photographed while out walking his dog in Los Angeles.
Eagle-eyed fans quickly noticed that the actor was wearing a t-shirt imagining Gatwa as the Doctor.
“Ryan wearing Ncuti as Doctor Who on his shirt… I’m dead,” one tweet read.
“Ryan Gosling wearing a Doctor Who shirt with Ncuti Gatwa on it has fully made my day,” another fan joked.
Davies, who will be returning as Doctor Who’s alongside Gatwa as showrunner, was also stunned by the moment, sharing the photo on Instagram.
“This is, genuinely, Ryan Gosling wearing a t-shirt of Ncuti Gatwa as Doctor Who,” he wrote, adding a shocked emoji.
He then cheekily added: “We’re suing him, of course. Illegal merch #RulesAreRules.”
It’s A Sin creator Davies showran Doctor Who when it was first revived in 2005.
He will return for its 60th anniversary special, which will also see David Tennant and Catherine Tate back on the show, as well as the future series from 2023.