Rumours have been running rampant that the 27-year-old actor is dating the stylist, reported E! online.
"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," a source said.
This isn't the first time that such rumours about Pattinson's love life have surfaced following his split from Kristen Stewart.
The most recent one came back in January, when he was romantically linked to London-based artist and painter Nettie Wakefield.