The 'Personal' group - which comprise Brad Simpson, James McVey, Tristan Evans and Connor Ball - are thrilled the 'Look What You Made Me Do' singer made her musical comeback this year and think they have a ''way in'' to making it happen.
James said: ''I am a massive Taylor Swift fan. It's really good to hear her having new music out. It would be awesome to collaborate. I don't know how we would get that working.
''We are on the same label actually. Maybe we would have a way in, we'd love to.''
And the group are also hoping to team up with EDM superstar Steve Aoki, but need to find the time to make it work.
James exclusively told BANG Showbiz: ''I spoke to Steve six months ago around the time when we released the song 'Middle of the Night'. We really want to work together but it is just quite difficult because he is so busy and we are as well.
''We are waiting for a song to come along, for us to write a song that would work with him.
''He's definitely interested. We've sent a couple of tracks back and forth to each other, but we are still working on finding the one that works. We'd love to work with him, he's a legend.''
The quartet recently teamed up with rising star Maggie Lindemann for their single 'Personal', and the American singer was thrilled to be involved.
She said recently: ''I love the song and the meaning behind it - I think everyone has gone through it. My manager and I were on our way to Norway and he played me a very rough demo of the song that only had Brad on it.
''I thought the concept was so cool! We recorded it a couple of weeks later. The Vamps were amazing to work with, super good energy all the time. They're cool guys!''