Smith told Collider that he would be intrigued to see the show's leads come together, but admitted that Sherlock co-creators Steven Moffat and Mark Gatiss are not fans of the idea.
"I think Mark and Steven kind of hate the idea of Doctor Who and Sherlock ever meeting," said the 30-year-old actor.
However, he added: "I'm not averse to it. I'm kind of open. I'm like, yeah [it could work], because I just think they would find each other so remarkable."
Back in 2010, Steven Moffat claimed that it would be "quite hard" to pull off a Doctor Who / Sherlock crossover but admitted that fan interest in the idea was high, suggesting that "everyone who's passing me in the street is suggesting that".
"I think there are problems of doing [a crossover]," he said. "Because then you would say that Sherlock Holmes lives in the same world as The Doctor, and there are Daleks and all sorts of things.
"If a Sherlock Holmes story depends on time travel being impossible, it's quite hard [to do it] if he's a personal friend of The Doctor's."
Doctor Who will return to BBC One this Christmas, while new episodes of Sherlock will begin shooting in January 2013.
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Watch a teaser trailer for the Doctor Who Christmas special below: