Elliott did not participate in Friday's walkthrough after sitting out practice Wednesday and Thursday to go through resistance training and rehab.
"The only chance he would have to play is if he keeps going on the right [path] that he actually has been going," coach Mike McCarthy said. "I mean he's doing a lot better than we anticipated. But if he practices tomorrow, then he'd have a chance of playing."
Speaking on 105.3 The Fan, Cowboys owner and general manager Jerry Jones seemed to indicate that Elliott would not play but did not completely rule him out ahead of the team's bye next week.
"I'm not so sure we'd have done it this way had we not had the bye. This just gives too good of an opportunity if we don't use Zeke," Jones said. "And we'll see how he is responding as the week goes along, but if we don't use him, this is just too great of a time to get him in top shape."
Elliott played most of last year with a torn posterior cruciate ligament in his right knee that limited his effectiveness, but he did not miss a game. Elliott, who took a helmet to the knee in last week's win over the Detroit Lions, has missed just one game in his career because of injury.
"I think he'll do outstanding and I'm anxious to see," Jones said of Pollard on 105.3 The Fan. "My vision of Pollard is that he can run all day. I don't know that I've ever seen him get tired. So he's got durability in terms of his ability to carry that load."
Linebacker Micah Parsons is expected to play Sunday after being listed as questionable and a limited participant for a second straight day with a shoulder strain. Defensive end Sam Williams (knee) is also questionable; he was a limited participant Friday after not practicing Thursday.
Safety Malik Hooker (hamstring), right tackle Terence Steele (neck), tight end Dalton Schultz (knee) and wide receiver Noah Brown (foot) are also questionable, although Hooker and Brown might be longer shots to play.