According to NFL Network's Ian Rapoport, the Cowboys and Peters are "working toward a deal," and it could get done by Monday.
Dallas brought Peters in for a visit last week after it was reported that starting left tackle Tyron Smith is most likely out until at least December because of a torn hamstring that came off the bone and required surgery.
Peters, 40, is a 17-year veteran who is best known for an 11-year stint with the Philadelphia Eagles from 2009 to 2020, although he began his career with the Buffalo Bills and most recently played with the Chicago Bears last season.
While he is way past his prime, he showed last season that he still had plenty left in the tank and he could be a good boost for a tackle-needy team like the Cowboys.