The two rock legends are keen to get in the studio together and hope they can lay down at least one track which they'll be able to release.
Paul said: ''We've talked about working together for a long time.''
Johnny added: ''We'd love to do it. We'll do a single together at some point, definitely.''
The pair were inspired to make music together after duetting on stage at their Teenage Cancer Trust concert last month.
The former Jam and Smiths members teamed up to perform a cover of Junior Walker & The Allstars' 60s hit '(I'm A) Roadrunner', and, while the two have shared the stage in the US a few times, this was their first joint stage appearance in the UK.
Johnny told NME magazine: ''I played with [Paul's '80s band] The Style Council hundreds of years ago when we were both children and then a few years ago in America, but this is the first time over here.''
Paul has previously revealed that he wants to work with Johnny, as well as Culture Club frontman Boy George.
He said: ''I'd like to do something with Johnny Marr. We were talking about it for a couple of years. We always bump into each other in different places, but we've never actually worked together. I'm up for working with anyone, really, if they're good. I'd really like to do something with Boy George.''
Billie Eilish thinks she may have taken it too far as she sees stars in her latest single release, 'NDA'.
Ed Sheeran channels a kind of vampire Joker in the video for his new electronic single ‘Bad Habits’; a song taken from his forthcoming album...