Gallup is seeking a second opinion before a determination is made on the surgery, according to sources, but the operation could happen as soon as Tuesday.
Gallup suffered the injury during the fourth quarter of Sunday's 31-21 victory over the Washington Redskins. While there was optimism after the game, further testing Monday revealed a cartilage issue.
Through two games, Gallup leads the Cowboys with 13 receptions for 226 yards. He had a career-high 158 yards on seven catches in the season opener against the New York Giants.
Austin did not play against Washington because of a concussion, but Smith caught three passes for 74 yards, including a 51-yard touchdown in the second quarter. Cobb has the most experience and has nine catches for 93 yards and a touchdown so far. Wilson opened the season on the practice squad but was called up for the Washington game to replace Austin.