He does not disclose her identity or her age, but says the age difference between them "would freak some people out".
Radcliffe, who has spent eight years playing Harry Potter, is soon to start a run of "Equus" on Broadway, New York, in which he plays psychiatric patient Alan Strang.
The 19-year-old actor will be on stage eight times a week, with full frontal nudity, just as he did in the hit London production.
He admits his current desire is to act as a drag queen. He would love to play a cross-dresser just so he could wear lots of slap and eye make up, he is quoted by Daily Mail as saying in an interview in the September issue of Details magazine.
The actor, known for his quiet life, says the role of Harry Potter has not left him with child star angst.
Radcliffe adds that he is currently single, and does not have room for a girlfriend in his life. "Most of my friends have been girls and I see how they are with their boyfriends and I think I couldn't do that. I just don't have the time, " he says.