Robert Pattinson: Dating Elvis's Granddaughter?

Buzz

By Tim Nudd

07/02/2013 at 01:35 PM EDT

Robert Pattinson and Riley Keough

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Robert Pattinson's has been spending quality time with is an up-and-coming actress who is rock royalty and, perhaps most intriguingly, friends with his old flame Kristen Stewart.

The Twilight actor, 27, was spotted driving around Los Angeles this weekend with Riley Keough, the daughter of Lisa Marie Presley and granddaughter of Elvis Presley.

Could it be a new romance – or just friends spending more time together?

Keough, 24, is no stranger to Pattinson's crowd. She acted with Stewart in the 2010 film The Runaways and attended her 23rd birthday party in April, along with Pattinson and a host of other friends, at the Malo restaurant in Silver Lake, Calif.

Keough previously dated English actor Alex Pettyfer, a.k.a. Adam from Magic Mike – to whom she reportedly was briefly engaged – as well as singer Ryan Cabrera.

Pattinson and Stewart split this spring after dating on and off for three years. They even initially survived Stewart's cheating scandal last summer with her married Snow White and the Huntsman director Rupert Sanders.

A source recently told PEOPLE that Pattinson is and now happily single.

A representative for Keough could not be reached for comment.