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.''
From their newest EP 'What Did You Think When You Made Me This Way', Nothing But Thieves drop the lyric video for their single 'Take This Lonely...
The Lumineers honour their friend and hero Tom Petty with a sensational cover of his 1996 song 'Walls' from the 'She's the One' soundtrack.
Watch Olly Murs get his nerd on as he blags his way into an exclusive Snoop Dogg party (where Rowan Atkinson is the bartender) in the video for their...
From 'Happy' to 'Banana Pancakes', these are soaked in positivity.
Mariah Carey is the picture of glamour in the black and white video for her brand new single 'With You'. It's the lead single from her forthcoming...
Eminem draws attention to the negative response his 2017 album 'Revival' received in the video for his latest song 'Venom'; a song recorded for the...
With the recent release of her third, very well received album 'Hunter' just behind her, Anna had plenty of relatively new songs to showcase.