Manager Don Mattingly doesn't see any reason why he can't.
"To me, Luis has come in and taken the job," Mattingly said. "That is my opinion. He's come in and said, 'Why not?' There is nothing he has done that says 'Don't play me.' He really has been great.
"Luis has definitely established himself, at the least -- the very, very least -- to be talked about as as far as an every day guy."
Cruz, 28, is batting .306 since being called up in July. Originally used at shortstop, Cruz shifted to third base and has committed only one error in 108 chances entering Saturday's game against the Rockies.
At the plate, Cruz's .326 batting average in 24 September games ranks 12th in the National League for the month, entering Saturday.
Cruz entered the season with only 56 big league games on his resume, after bouncing around several organizations.
The Dodgers control Cruz's contract through 2014, and it wouldn't be a surprise to see his name penciled into the Opening Day lineup in 2013.
"When we first started Cruzer, I really kind of thought, honestly, that he was going to get exposed at some point and hit a cold spell," said Mattingly, who compared Cruz to Casey Blake. "He's shown nothing but being able to handle everything we've given him."