The couple was seen dining at Wolfgang Puck’s famous Beverly Hills restaurant, Spago, over the weekend.
Rumors that the two were dating began when they started work on Vanilla Sky.
In the past, Cruz has been vocal about the media linking her romantically to her costars.
“Just because we are actors, it doesn’t give anyone the right to ask who we sleep with,” Cruz told the Calagary Times in April. “It’s such an absurd invasion of privacy, which is why actors lie so much about their private lives. It’s our way of getting back.”
She also made it a rule when she became famous to not talk about her private life.
“I won’t break that rule now just to put those rumors to rest, ” she told the Calagary Times.