Medical tests Wednesday showed that Ware, who did not practice because of a strained neck, has no structural damage and is close to having a full range of motion. An MRI and an X-ray showed swelling had gone down.
There is a chance he could practice Thursday.
"What our final decision is going to be is based on whether it's a chance he will get banged up again," coach Wade Phillips said after Wednesday's practice. "Structurally he's not in any danger. He doesn't have a disk or a broken neck."
Ware, who leads the team in sacks (nine) and quarterback pressures (37), has lifted weights the last two days.
"It's still day-to-day as far as him completely being cleared," Phillips said. "Again, he's close. Again, he wants to play. We want him to play, but we are going to be cautious, too."
Phillips said he's comfortable with Ware playing if he doesn't practice this week. He also didn't rule out limiting Ware's snaps if he does play. The Cowboys will practice red zone drills Thursday before leaving for New Orleans on Friday afternoon.
This is Ware's second neck injury of the season. He came out of the season opener against Tampa Bay on the first defensive series. He returned and finished the game with seven tackles and three quarterback pressures.
Ware said the first injury occurred because he didn't wear a neck brace attached to his shoulder pads.
"I had that injury, and I came back from that," Ware said Tuesday. "I feel better from this injury than I did from the first one, which is weird. I had a lot of people praying for me."
It's been a frustrating season for Ware, who also has played with a stress fracture in his foot and a chipped bone in his wrist.
"It's just another thing," Ware said. "They took me off the injury report and stuck me on there for something else. So I'm going to do what I need to do to get ready. It's up to the trainers' decision to make sure it's the right decision at the time and for myself."
In other injury news for the Cowboys, free safety Ken Hamlin (right ankle sprain) was limited in practice but still could play. Tight end Martellus Bennett (concussion) didn't practice and will miss a second consecutive game.