The 'Called out in the Dark' group have a lot of respect for the 'Bad Romance' hitmaker and would love to get her into the studio to add something different to one of their songs.
Drummer Jonny Quinn exclusively told BANG Showbiz: "I think she's pretty incredible. To get her to guest vocal would be a coup.
"I love watching her and reading her interviews. She knows exactly what she's doing, she seems so much smarter than your average pop star and is really talented.
"I've seen those early videos of her playing New York gigs, she's just an amazing keyboard player, great musician, great writer, she's the whole deal."
The only thing which would make the band hesitant to work with Gaga, however, is the fact that Coldplay recorded the track 'Princess of China' with Rihanna, and the group are worried people would think they were "copying" them.
Among their other rock star friends, Snow Patrol count funk band Red Hot Chili Peppers, but they're not sure if trying to marry their very different styles would have great results.
Johnny added: "We know the Chili Peppers they're really good guys, I know Chad the drummer quite well but I don't know if us collaborating with them would work out."
Snow Patrol's sixth album 'Fallen Empires' is out now.