Rapoport reported that Sturgis will be placed on injured reserve/designation to return after the kicker sustained a hip flexor injury in Philadelphia's season-opening 30-17 victory over the Washington Redskins on Sunday.
Elliott, who lost a competition to Randy Bullock this summer, was selected by Cincinnati with a fifth-round pick in the 2017 draft. He made 21 of 26 field goal attempts last season with Memphis, including two of three from outside of 50 yards.
Sturgis was injured early in Sunday's win but was able to stay in the game. After the contest, coach Doug Pederson said it was why the Eagles went for a two-point conversion following their last touchdown.
After Philadelphia's last touchdown, Sturgis appeared gimpy walking off the field following the kickoff.
Sturgis converted field goals of 50, 42 and 37 yards in Sunday's game.
In his first two seasons with the Eagles, Sturgis converted 53 of 63 field goal attempts and 65 of 68 extra point attempts.
A fifth-round pick of the Miami Dolphins in 2013, the 28-year-old has converted 81 percent (111 of 137) of field goal tries and 97.2 percent (140 of 144) of his extra points in regular-season games.