The Muse frontman - whose property in Italy's Lake Como neighbours that of the Hollywood actor - admitted he was hoping to get invited round for a spot of gambling because he was confident he could win some money off him.
He said: "I have seen him cycling back and forth, he likes his bicycle. I was hoping for an invitation to play poker. I'll take him on, heads up, 10 grand a piece. I'm good enough at poker to take on someone like him. Or he could come round mine for some freeze-dried Bolognaise."
The 30-year-old musician struck up a close friendship with Lily Allen when they performed together in Australia, and says they enjoyed seeing the sights of the country when they were off stage.
Speaking about his relationship with the 'Smile' star, he said: "We had a few nice days out, had a little chat about the music business."
Matt also claimed he is just as confident - although not as lucky - with the older women too.
He added in an interview with Q magazine: "Jane Fonda. She's 72. I like the older ladies, you see. She was hanging around with Rod Stewart the other day. She seemed like a nice lady. But I failed - I didn't charm her enough."