updated 09/26/2013 AT 3:30 PM ET
•originally published 09/26/2013 AT 1:30 PM ET
Has Robert Pattinson found a new leading lady?
“They’ve been dating a month or two,” a Pattinson source confirms to PEOPLE. “He’s crazy about her.”
The blonde beauty, 22, has quite the Hollywood pedigree: She’s the daughter of Sean Penn and Robin Wright.
According to media reports, Pattinson and Penn were spotted on Sept. 7 catching a show by rapper Mickey Avalon at the famed Viper Room in Los Angeles.
They then reportedly hightailed it to the Chateau Marmont for post-show drinks and bites.
Speculation has been swirling about whom Pattinson would date next following his split with Stewart. He was also recently seen with trainer Sydney Liebes outside Harley Pasternak’s gym, where she works. But a second source shoots down any insinuation that the two are an item, telling PEOPLE that “Pattinson has trained with Liebes a few times in Harley’s absence and that s it.”
In May, Pattinson and Stewart, 23, called it quits after more than three years of dating, their relationship having weathered intense strain and scrutiny following her fling with her married Snow White and the Huntsman director, Rupert Sanders.
The two had attempted to patch things up following her cheating scandal, attending Coachella and celebrating her 23rd birthday together before ultimately calling things off. On May 21, Pattinson was seen moving his belongings out of Stewart’s Los Angeles home.