The 'Cosmopolis' actor is said to have struck up a close relationship with the 'Roar' singer's "super stylist" and confidant Cleo Wade, and they all spent the majority of Coachella Valley Music and Arts Festival together over the weekend.
A source told The Sun newspaper: "Cleo is one of Katy's best friends, so Rob has been spending time with their gang. It's early days but they seem to have good chemistry. They spent a lot of time together over the weekend."
The reports will put an end to rumours that Katy,29, had been dating the 'Twilight' hunk following her split from John Mayer.
Katy - who was previously married to Russell Brand - has previously dismissed speculation of a romance with Robert by explaining she has a "big sister" relationship with the 27-year-old actor.
She said: "He's my bud, I'm like his big sister. We just hang out. The other day, I said, 'One of the things I'm most proud of is not sleeping with you, Robert'. And that's true."
As well as Robert, the 'Part of Me' hitmaker was recently romantically linked with Diplo as they appeared to be "more than friends" at a Coachella party earlier this month.