The former Oasis singer - who recently revealed he wants to head back out on the road, two months after the group split following The Departure of his guitarist brother Noel Gallagher - has befriended the Last Shadow Puppets star, who said he hopes the 'Live Forever' hitmaker will team up with him on his new solo LP.
Miles told NME magazine: "I was chatting to Liam at his party. He's my hero and we both love Lennon and we were just chatting about my record and what he's up to.
"I've got a couple of tunes on my record that are very Liam, there's 'My Fantasy', which he'd be great singing on, who knows, leave it open."
Liam recently revealed he is currently working on new material with Oasis bandmates Gem Archer, Andy Bell and Chris Sharrock.
He said: "We're sort of doing things at the moment. Not Oasis, Oasis is done. But with everyone except for Noel."