The 80s pop legend was invited by the group's frontman Dave Grohl to join them onstage at Japan's Summer Sonic Festival last August, where they played Nirvana's 'Smells Like Teen Spirit' before breaking into his biggest hit, and they've reunited on several occasions, most recently at Reading Festival this summer.
Rick feels that their duet lives in a ''moment'', but he'd consider recording their version for a worthy cause.
He told the Daily Star newspaper's Wired column: ''I would be well up for releasing it, maybe for charity one day. The amount of people who say we should but they have bigger fish to fry and also I like that it's ''a moment''.
''I've done it three or four times now but it's always an accident. It exists in an alternate universe.''
Meanwhile, the 'Cry For Help' singer is planning to send a crate of his new Astley's Amber Ale to the 'Everlong' band's studio to loosen them up before working on their new record.
Rick - who has just launched his third alcoholic beverage with Mikkeller brewery - said: ''Dave Grohl likes beer. I will send a box to their studio in LA while they are recording.''
The British star still has ''no idea'' why he was invited to perform with the US rockers.
He said recently: ''It just all went nuts.
''Dave Grohl came over and said hello, gave me a hug, and then half an hour later he's inviting me onto the stage.
''I never met them [before], I have no idea why he'd invite me onstage. I didn't know what it was all about. And then he just kind of whispered and said, 'We're doing your tune, but we're gonna do it like 'Teen Spirit'', and that was it. And off we went.''
Rick previously admitted he would love to collaborate with the band in future.
Asked if there could be a Rick Astley and Foo Fighters song in the pipeline after Justin Timberlake recorded vocals on 'Make It Right' on their last LP 'Concrete and Gold', he told BANG Showbiz: ''There you go. It's funny that actually. I think it is really brave when artists like that do that.
''You might upset the audience, the critics etc. I think they just think, y'know what we are doing it.
''He's in the studio next door, we are doing it.
''I am going to try and write with some other people because I want to experience that.''
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