In fact, a source tells me, they have yet to refer to each other as "boyfriend and girlfriend."
"But it is a romance," the source said, adding that neither is looking to speed things up.
The Twilight star and model daughter of Sean Penn and Robin Wright appear to be well suited for each other.
"Dylan doesn't want to be famous," the source said. "She doesn't want to be an actress. She wants to be a screenwriter. She's been approached about acting work, but it's not her thing."
And she's not a party girl. "You won't seen her becoming a regular at Bootsy Bellows," the source said, referring to the late-night celebrity hot spot in L.A.
But we will see more of her very soon. Penn was recently shot for spreads in two major magazines.
Rumors that Pattinson and Penn were hanging out first surfaced in September when they were spotted together at Chateau Marmont in West Hollywood after seeing a show by rapper Mickey Avalon.
Fast-forward to this Wednesday—the two were at a private party celebrating the release of Angie Banicki's new book 30 Before 30 at the Hollywood Roosevelt Hotel.