According to The People, the Love Actually star says he turned down the offer as he was not ready for the intense media attention it would entail.
Nighy is quoted as saying: "I was offered the role once, I won't tell you when because the rule is that you're not allowed to say you turned that job down because it's disrespectful to whoever did it. I will say that I was approached.
"But I didn't want to be the Doctor. No disrespect to Doctor Who or anything. I just think that it comes with too much baggage."
Nighy appeared a small uncredited role in the Doctor Who episode 'Vincent and the Doctor' two years ago, playing an art gallery curator opposite current Doctor Matt Smith.
Christopher Eccleston, who left the show after one season, also suggested that the media attention associated with the role was too much for him.
Eccleston has ruled out a return for the 50th anniversary of the show next year.
Watch a press call with Doctor Who star Matt Smith below: