Pattinson is not ready to move in with Stewart yet
The couple briefly split up last year after Stewart cheated on him with married director Rupert Sanders, reported Hollywood Life.
"Robert's still taking things slow with Kristen. They're not buying a house together. That's just ridiculous. They're having fun and taking it day by day," a source said.
"Robert would never put that kind of pressure on things right now. Plus, he's still making Kristen prove herself. Plus, Robert's really focused on work right now. His career is his priority, not shopping for a house," it added.