The 46-year-old sticksman says the former Oasis frontman - who is a massive fan of his 2016 solo track 'Range Rover Bitch' - hasn't asked him to play for him yet, but Liam is aware Taylor is keen to write a song with him.
Asked if he'd like to join Liam's touring band - which includes Babyshambles bassist Drew McConnell - on percussion, Taylor told Matt Wilkinson on Beats 1: ''Absolutely. He hasn't asked. He loves [Taylor's track] 'Range Rover Bitch' - that's so amazing! I'd like to write a song with him. If he likes 'Range Rover Bitch' man. I've already told him that, he knows. He's such a character.''
Taylor admits that he wasn't as fond of Liam's band he started after Oasis split in 2009, Beady Eye, but he loves his solo stuff from his debut LP, 'As You Were', and the fact he can be a ''temperamental performer''.
He said: ''I think for him, having the new band Beady Eye was just confusing to people and now he can be Liam Gallagher which means he can play all the Oasis songs he wants and he can play his new album, which is really the best music he's made since Oasis.
''I heard a few Beady Eye things and it was good but he knows he needs to write songs with other people.
''I'm stoked for him.
''And when he's on man, he's on! That's what I love about him, he's such a temperamental performer.''
Liam turned down the chance to duet with the 'Best of You' group last year.
The 'Songbird' songwriter was invited by frontman Dave Grohl to join them on the Pyramid Stage, but Liam declined because of the lack of time for rehearsals.
The 'Greedy Soul' singer said at the time: ''He asked me to come on and do a song. I said no, cos I need a bit of rehearsal. I know it's cool and all that, but I need a rehearsal.''
However, the rocker said he would've loved to have done a duet with Taylor on 'Range Rover Bitch'.
He said: ''I tell you what I wanna do. I wanna do 'Range Rover Bitch' that Taylor [Hawkins, drummer] made. That's the tune.''
Liam did end up performing with the 'Run' rockers at their own festival, CalJam, in San Bernadino, California, last October, where they teamed up on a rendition of The Beatles' hit 'Come Together'.