The two singers will likely release new albums this year and both of them were approached for the Olympic gig, reported Ace Showbiz.
Blind Gossip, a site that publishes celebrity rumours without taking names, recently posted a story about a "recent situation involving two famous singers who can't stand each other."
"Well, she blew it again! She was one of several singers in competition for a song for a major sporting event, but she just couldn't rise to the occasion and come up with a song that would work," read a post on the website.
"However, she is definitely the one who feels most burned by the winner! That's right. Losing is bad, but losing to Winner - the person with whom our singer has so much bad blood - was just infuriating!" the site added.
Neither Swift, 26, nor Perry has responded to the rumour yet.