Murray is not expected to play Sunday against the Philadelphia Eagles because of a sprained medial collateral ligament in his left knee. Dunbar missed the Washington Redskins' game with a hamstring injury and was unsure he would be able to practice this week.
Rookie Joseph Randle and Phillip Tanner are the only healthy running backs on the 53-man roster. Randle is expected to get the bulk of the work in Murray's absence. He had 11 carries for 17 yards and a touchdown against Washington.
Meggett was with the Indianapolis Colts in the summer but was cut in August. He was with the Houston Texans for a time in 2012. The son of former NFL running back Dave Meggett ran for 2,411 yards at Maryland.
It is possible he could be a late-week call up to the active roster if the Cowboys want to have a third runner on the game-day roster.