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 & Harry Potter 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."