The 61-year-old actor is currently working on an album following his Oscar success as alcoholic country singer Bad Blake in Crazy Heart last year, and is keen to work on a track with the music icon.
He told Shortlist magazine: “Winning the Oscar has helped me. I'm currently making an album with producer and songwriter T-Bone Burnett. That comes directly from the success of Crazy Heart.
“I was recently on the 'Speaking Clock' tour, headlined by Leon Russell and Elton John. Elvis Costello was there and I got to sing with him, which was cool, I really enjoyed it.
“Elton is a great person. We talked about doing a duet. I'd certainly like to.”
Discussing his Oscar success - this year repeated with a nomination for his role in True Grit - the bearded star reveals his favourite thing about awards recognition is the 'acknowledgement' of his peers that he has made a good movie.
He said: “It's great to be acknowledged by the guys for what you do. There's also an element to all of these award shows that they're a commercial for the movie industry.
“That's not necessarily a bad thing. There's an element of my job that's like being a barker at a carousel. But after you put all that energy into a film, it's great if people come see it.”
