The band - which also includes Miles Kane, Jet's Nic Cester, Jamie Davis, and Sean Payne of the Zutons - started off as a "bit of fun" and Muse star Matt admitted he's enjoyed not having the "pressure" to write new music.
However, they haven't ruled out the possibility of making their own material in the future.
Blur guitarist Graham told The Sun newspaper: "I’ve thought about how it would go and what direction it would be. I’d be up for putting some demos forward.”
And Matt - who is actively working on new stuff for Muse's follow-up to 2018's 'Simulation Theory' - added: “Writing our own songs could happen one day.
“But at the moment we’ve enjoyed having no pressure to do that kind of stuff. We’ve enjoyed treating it more like the way DJs put together a set. It’s a different approach and one thing that sets us apart in a way.
“We could go down the road of doing songs but I personally like the idea of digging up music from the past. I’ve started writing a new Muse album as well.
“I started writing when all the protests and all the chaos were kicking off. It’s a weird thing to say but it suits the music I write. It keeps you a little bit on edge.”
The supergroup have played a select number of gigs, including a house party, Stella Mccartney's fashion show and the Teenage Cancer Trust at The Royal Albert Hall.
The Jaded Hearts started out covering Beatles songs and have recently expanded their repertoire and released a record of covers of "lost" greats, including Northern Soul and Motown tracks, on the LP 'You've Always Been Here'.
Matt recalled the time Beatles legend Sir Paul McCartney joined them on stage for a cover of The Beatles hit 'Helter Skelter' at his daughter Stella's show in Los Angeles in 2018, and said it was like being in the 'Get Back' group.
He recalled: “It wasn’t planned, (it was) totally random.
“Paul just jumped on stage and started singing with us. For that one moment, we thought, ‘Hold on a minute . . . we are The Beatles!’”
From Her To Eternity is the foundation stone that paved the way for Your Funeral...My Trial, Henry's Dream, Murder Ballads, Push The Sky Away,...
Noel Gallagher reckons no-one likes a do-gooder. He’s so wrong.
David Bowie fans across the globe have something very special to celebrate today as it has just been announced that the worlds's first David Bowie...
In a recent open letter to the Prime Minister, Boris Johnson, major players in the UK music industry, including Sir Mick Jagger, Sir Paul McCartney...
Megan Thee Stallion pulls no punches and is unapologetically outspoken on her latest single, 'Thot S**t'.
Hollis Lomax; consisting of Will Rowland (Keyboard/Vocals) Hugo Keays (Guitar) Will Ellis (Bass Guitar) and Rob Taylor (Drums), are excited about...
There is nothing more uplifting in this world than watching Billie Eilish - the face of moody teen angst - having so much fun in the video for her...