Nonetheless, Cowboys owner Jerry Jones is positive the team can come to terms with Elliott, who is currently holding out in search of a new contract.
"(I'm) optimistic that we can get Zeke's deal done," Jones said, according to Rob Phillips of DallasCowboys.com.
"I don't know that. I don't know that. But sure, I don't mean to be trite, but the whole premise is based upon getting everybody under contract playing, so that's what we're trying to do here.
"I don't want to sound like it's not important for him to be here. I think it is important for him to be here or we wouldn't be having everybody be here, everybody getting some work in. Everything about this is important. Everybody does understand it. It's just a question of seeing if it works, but you know, we're going to play football one way or the other. That's the way it works."
The Cowboys have one preseason game remaining against the Tampa Bay Buccaneers on Thursday before they host the New York Giants in the season opener Sept. 8.
Elliott did not play in the preseason last year and finished as the league's rushing leader. He opened the campaign with 69 yards on 15 carries in a Week 1 loss to the Carolina Panthers.