Speaking to WhatsOnStage recently, the 23-year-old star, who appeared on Broadway in 2011 in How to Succeed in Business Without Really Trying, said he would "love" to do a musical in the West End.
"If [the show] was the right one I would love to do it," he said. "There was talk about How to Succeed coming to the West End after Broadway but at that point I had done it a year and my heart wouldn't have been in it at the time."
And Radcliffe, who won WhatsOnStage Award in 2008 for Equus, revealed he also has an eye on some big roles in the drama canon, including the biggest of them all, Hamlet.
"It's something any actor would want to do and it's very intimidating thinking about all those who have done it before you and all those I have seen do it," he said. "It's hard to imagine at the moment but it is also one of the greatest parts in all of literature so yes, I would jump at the chance."
Of modern plays, he said: "Rosencrantz and Guildenstern Are Dead by Tom Stoppard is one of my favourite plays, and another Irish play that I absolutely love is Translations by Brian Friel. I'd also love to do Waiting for Godot, but I'll have to wait til I'm an old man."
More immediately, he is reportedly soon to branch into pop with a guest vocal on a new single from eccentric band The Duckworth Lewis Method.
According to the Evening Standard: "Radcliffe joined fellow celebrity cricket fan Stephen Fry and commentators Henry Blofeld and David Lloyd on Sticky Wickets, the follow-up to the debut record by Irishmen Thomas Walsh, of the band Pugwash, and Neil Hannon, from The Divine Comedy, who paired up to make it. And 'Third Man', the track on which the Harry Potter star has a speaking role, is now set to come out as a single."
Our sold out WhatsOnStage Outing to The Cripple of Inishmaan takes place tonight (24 June 2013) - don't miss live tweeting from the post-show Q&A with cast members including Daniel Radcliffe