Yates - who directed Radcliffe in his final four Harry Potter outings - confirmed the project late last year, revealing that he planned to spend "two to three years" working on taking the BBC series to a "bigger arena".
When asked if he would be interested in playing the iconic role, the Woman in Black star sought reassurance from his team that the news was "out there".
"I don't know if I could play him," Radcliffe told Digital Spy. "Matt Smith plays Doctor Who and does a wonderful job. They don't need me!"
He continued: "I would never presume to jump into somebody else's franchise, not at all."
However, the 22-year-old said that he is confident Yates will "do a wonderful job" with the film, adding: "I'm sure whoever he casts will have a very good time with him."
Radcliffe next stars in The Woman in Black, which opens in cinemas on February 10.
> 'Doctor Who' movie: David Yates not yet looking to cast The Doctor
> 'Doctor Who' movie will not be a reboot, says Steven Moffat