By Kev Geoghegan
Radio 1 music reporter
The band met McCartney at their graduation ceremony in Liverpool
The Wombats say they are "ridiculously flattered" that Sir Paul McCartney wants to produce an album for them.
The former Beatle made the offer during an interview with BBC 6 Music before his Liverpool Sound concert on 1 June.
He said: "I don't do much production now but it might be very tempting. I'm not sure they would want me."
Wombats drummer Dan Haggis said: "It's ridiculously flattering to have a Beatle like Sir Paul even mentioning us in a sentence."
"We were laughing about it, like it would be an interesting collaboration.
"I think we'd be up for doing a demo and seeing what it was like.
"Imagine kicking back with Sir Paul? Like, 'Yeah, I think we need a bit more hi-hat there Paul.'"
The Liverpool-based band already have a fledgling relationship with Macca, having attended the Liverpool Institute of Performing Arts.
McCartney said: "I had one of the guys in one of my classes. It was great. Now, years later they're doing great."
Haggis admitted his one meeting with Macca, during his graduation, was particularly memorable.
He said: "He hands out the diplomas and degrees so I did get to shake his hand.
"I had an eyebrow piercing in at the time and he said, 'We'll have to get a screwdriver for that.'
"I was like, 'Okay, whatever you say!'"
The Wombats headline the first day of the Beach Break students festival in Cornwall on Monday.