Latest gossip suggests the pair got up close and personal at the after party for Rob's new film The Rover in LA. The duo were spotted "flirting" before Robert - who is thought to be seeing New York-based stylist Cleo Wade - confessed to his mates that he thinks Katy is totally "hot".
Whoa there horsey! Just writing that little titbit made us all hot under the collar.
A source, who allegedly witnessed the pair's interaction at the W Hotel, told the New York Post's Page Six there was some "heavy" flirting going on.
If the rumours turn out to be true we will have officially found the most unlikely couple in La La Land.
Katy recently told Elle magazine that there was absolutely nothing going on between Kristen Stewart's ex and she.
"He's my bud, I'm like his big sister. We just hang out," she said and even went as far as telling the Brit actor how proud she was she hadn't ended up in between the sheets with him.
"'One of the things I'm most proud of is not sleeping with you, Robert.' And that's true," she added.
However, Katy also revealed they're not actually an item.
"Here's the proof there was never anything going on with me and Robert Pattinson. I fart in front of him. Properly fart. And I never, ever fart in front of a man I am dating. That's a rule."
LOVE KATY? See more from the songstress in the gallery below.