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'.
' 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: 't'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.'