Bailey suffered the injury while kicking into the net during Sunday's 40-10 win against the San Francisco 49ers. Safety Jeff Heath took over the kicking duties for the rest of the game, making 2-of-3 point-after attempts.
Speaking on 105.3 The Fan in Dallas on Monday, executive vice president Stephen Jones all but ruled out Bailey from next week's game against the Washington Redskins, saying, "This could be more than a week at a time."
According to ESPN Insider Field Yates, the Cowboys will work out Mike Nugent, Jason Myers and Sam Irwin-Hill.
Bailey, the most accurate kicker in NFL history, has made all seven of his field goal attempts and all 16 extra points.
Nugent, who was beat out by Aldrick Rosas for the New York Giants this summer, has the most experience. In 12 seasons, including seven with the Cincinnati Bengals, Nugent has made 236 of 292 field goals (80.8 percent).
Irwin-Hill went to training camp with the Cowboys and was among their final cuts. He made all seven point-after attempts and made 2-of-3 field goal tries. He has yet to kick in a regular-season game in his career.