BBC
Showrunner Steven Moffat said that an offer was given to a black actor after Matt Smith, the 11th incarnation of the Doctor, stepped down in 2013.
Moffat, who didn't name the actor, told the show's official magazine that "for various reasons, it didn't work out."
Scottish actor Peter Capaldi ended up getting the coveted role. But the producer still thinks casting a non-white actor in the role is important.
"I certainly don't think there's ever been a problem with making the Doctor black, which is why it should happen one day," Moffat said.
"Sometimes the nature of a particular show - historical dramas, for instance - makes diversity more of a challenge, but 'Doctor Who' has absolutely nowhere to hide on this," he added.
In April, "Doctor Who" announced that it was replacing actress Jenna Coleman, who decided to leave the show last year, with black actress Pearl Mackie as the Doctor's companion.
"We decided that the new companion was going to be non-white, and that was an absolute decision, because we need to do better on that. We just have to," Moffat said of the casting. "I don't mean that we've done terribly - our guest casts are among the most diverse on television - but I feel as though I could have done better overall."
And even with a non-white actress playing the companion, Moffat hasn't shelved his desire for a non-white Doctor in the future.
"Two non-white leads would be amazing," Moffatt, who's leaving the show after one more season, said. "In fact, a lot of people would barely notice."