It was reported last week that Harry Potter director David Yates is to helm a "radical" film reboot of the popular sci-fi drama.
"I have absolutely no idea what it will be about," Smith told host Fearne Cotton on her Radio 1 show. "We're not really anything to do with it."
The actor added that he had no clue the film was in development, explaining that both he and co-star Gillan had "read [the news] in the paper".
"There's always rumours about a Doctor Who film," suggested Gillan, who plays companion Amy Pond. "I remember them saying that Johnny Depp was going to be the Doctor."
Both stars went on to say that they "doubt" they will appear in any potential Doctor Who film.
Doctor Who will return to BBC One this Christmas.
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Watch a trailer for the Doctor Who Christmas special below: