Rapoport added the Patriots "would like to bring him back, but that's up in the air now."
The Patriots selected Fleming in the fourth round of the 2014 draft, and he proved to be a solid reserve who stepped up and provided quality snaps at various positions across the line.
The Stanford product made 47 appearances, including 20 starts, over his first four NFL seasons. In 2017, Fleming made six starts and played 369 total offensive snaps.
If the Cowboys hammer out a deal with Fleming, they'll be in a position to shuffle some pieces around.
According to ESPN.com's Todd Archer, the Cowboys could install Fleming at right tackle and shift La'el Collins over to left guard, which is where he was stationed for his first two seasons.