Mare, a 16-year NFL player, won a tryout against veterans Billy Cundiff and Neil Rackers and younger kickers Garrett Lindholm and Justin Medlock and was signed to a one-year contract, the Chicago Tribune reported Wednesday.
Gould, the fourth most accurate field goal kicker in NFL history at 85.6 percent, suffered a calf injury in warmups before the Bears' 21-14 loss to the Minnesota Vikings in Minneapolis Sunday.
Mare, who played for the Carolina Panthers last season, has made 81.2 percent of his field goal attempts in his career with the Seattle Seahawks, the New Orleans Saints, Miami Dolphins and the Panthers, the newspaper said.
Bears starting quarterback Jay Cutler, who left the game against the Vikings with a stiff neck, indicated he is ready to play in Sunday's home game against the Green Bay Packers.
2014: NFL Cheerleaders [PHOTOS]
Arizona Cardinals player formally charged