The Rennes forward, 25, has been linked with a £34million move to the Premier League after hitting 12 goals and five assists for the French club this season.
The latest of those strikes came in the clash with Nice but Terrier was forced off with a potentially serious knee injury after 35 minutes.
Manager Bruno Genesio told reporters: “For the moment, his knee has swelled well but we don't have a diagnosis. It's too early to have a reliable one.
“We didn't talk too much about that at the break, but all the players went to see Martin in the physio’s room to comfort him.
“A twisted knee that swells up is never a very good sign, but for the moment I can't tell you more.”
Liverpool had also been touted to make a bid for Terrier but have already signed Cody Gakpo, leading to United intenisfying their search for alternatives.
Midfielder Benjamin Bourigeaud described his sadness at Terrier’s injury before scoring Rennes’ late winner.
He said: “After his injury, we got together to say that we were going to play for him… When he came out, I shook his hand. He told me to win the game. I told him we would do it for him.
“We felt sad and downcast in the dressing room. It can be serious.”