The 'Still Alice' actress, 24, and the model-actress, 23, met at Paris hotspot Chez Castel, where Stewart was hanging out with some close friends, reported Us magazine.
"They were laughing, talking, and even dancing together all night. They looked like they became friends," a source said.
Penn - the daughter of now-divorced actors Sean Penn and Robin Wright - was first linked to Pattinson back in 2013, a few months after he and his 'Twilight' co-star ended their tumultuous four-year relationship.