Parker sat out for the second half of the Dolphins' 16-10 win against the Titans on Oct. 8 and did not play at all in the Dolphins' 20-17 win against the Atlanta Falcons last weekend in Atlanta. The fourth-year pass catcher suffered the injury in the first quarter of the Oct. 8 matchup.
After leaving the game with the injury, Parker briefly stayed in the locker room. He reemerged without wearing his helmet and attempted some running and cutting on the sideline while talking with the team's medical staff. He never went back in the game and was ruled out at halftime.
"We still just keep holding out hope," Dolphins offensive coordinator Clyde Christensen told reporters Thursday. "He's had some Lazarus experiences out there where he's showed up at the last second from the dead, so we still keep hoping. We're so used to it now. I'm not saying that to be cute, we're just used to it."
Dolphins coach Adam Gase said that he didn't know if Parker would be doing anything at practice. He also said that Parker is "day to day."
Parker, 24, has started 16 of a possible 37 games since being picked with the No. 14 pick overall in the 2015 NFL Draft.
The Dolphins face the New York Jets at 1 p.m. Sunday at Hard Rock Stadium.