Sunday marked the first day the Cowboys could have placed Romo on injured reserve, which means he would be able to return later in the regular season.
To make room for Sanchez, the Cowboys waived quarterback Jameill Showers.
If the Cowboys choose to place Romo on injured reserve, he would miss the first eight weeks of the season and be eligible to play Nov. 6 at the Cleveland Browns.
The longer they take to make a roster move, the more likely it is they will carry Romo on the active roster and deactivate him each week until he is healthy.
After Romo suffered a compression fracture in his back on Aug. 25 in a preseason game against the Seattle Seahawks, sources said he would need 6-10 weeks to recover. The Cowboys are weighing whether he could return a week or two before he would be eligible to return from injured reserve.
The Cowboys play at the Green Bay Packers on Oct. 16 in Week 6 and have their bye week on Oct. 23. They host the Philadelphia Eagles on Oct. 30.
Romo suffered a compression fracture of his L1 vertebra when he was driven into the turf by Seahawks defensive end Cliff Avril as the QB was going into a slide. Romo wanted to re-enter the game but the coaches held him out, and an MRI the following day revealed the fracture.
He is scheduled to be in a back brace for another week.
Rookie Dak Prescott will start in Romo's absence, and Sanchez, who was cut Saturday by the Denver Broncos, will be the backup.
The Cowboys came to an agreement with Sanchez on a one-year deal on Saturday.