"We just don't want to do anything that would put him in some kind of category that would limit us from getting him in the first game," Jones said before Wednesday's practice.
Gallup, who tore the ACL in his left knee in January and had surgery in February, has said he would not be able to play in the Sept. 11 opener against the Tampa Bay Buccaneers, calling it "not realistic" last month. But not being placed on PUP would allow him to return later in the month.
He currently is on the active/physically unable to perform list, and if the Cowboys move him to reserve/PUP at the final cuts next week, he would be forced to miss the first four games.
Gallup started running routes last week as he stepped up his rehab.
Coach Mike McCarthy said later Wednesday that Gallup has not had any setbacks in his recovery, but he was not ready to make roster decisions publicly before Friday's preseason finale against the Seattle Seahawks.
"We've got to play this last game," McCarthy said. "There's young guys that are battling for spots, how that 53 comes together. Obviously we don't want to take away Michael's opportunity to play as soon as possible, but how that comes down at the end, that's really to be determined."
Gallup has worked daily on his recovery with director of rehabilitation Britt Brown.
"[Brown] feels real good about Michael's progress as far as his timeline and so forth," McCarthy said. "He hasn't had any setbacks, and I hope we will continue to be blessed with that process. He's doing really well."
The Cowboys re-signed Gallup to a five-year, $57.5 million deal in March, despite knowing he would need to be eased into the regular season following the surgery. He was limited to eight games in 2021 because of calf and knee injuries, finishing with 35 catches for 445 yards and two touchdowns.
Despite trading Amari Cooper to the Cleveland Browns and losing Cedrick Wilson to the Miami Dolphins in free agency, the Cowboys opted not to add a high-priced free agent, knowing Gallup would be back sooner rather than later. Veteran James Washington signed a one-year deal in free agency, but he suffered a broken foot in the first week of training camp.
While the Cowboys know what they have in CeeDee Lamb, who will move into the No. 1 receiver role with Cooper gone, they spent the summer looking at younger receivers, like third-round pick Jalen Tolbert, Noah Brown, Dennis Houston (an undrafted free agent), Simi Fehoko (a fifth-round pick in 2021 who did not have a catch last season) and KaVontae Turpin (the USFL MVP this spring).
"I feel better than when we initially did in training camp," Jones said of the group. "I really like the entire gambit of our receivers. We've got some things to scratch, head-scratch, with the numbers there. We certainly at this juncture don't have room for an outside receiver."