Striker Hamza Igamane has failed to train with the Rangers squad ahead of Wednesday's Champions League play-off game against Club Brugge.
Sky Sports News understands the 22-year-old is not injured, with the club believed to be preparing for life without the Morocco international.
French club Lille want to sign the player, who refused to come on as a second-half substitute during Rangers' draw away to St Mirren after claiming he was injured.
It is understood the Ligue 1 side have held fresh talks and are expected to table another bid, after their first offer for a loan deal was turned down last week.
However, Dutch team Feyenoord are also keen on Igamane, who scored 16 times in his first season at Ibrox.
No deal has been agreed for the player to depart Glasgow, with Rangers expected to hold out for the right fee if they are to sell the player.
'We need people to be all in'
Speaking after Sunday's game, Rangers head coach Russell Martin told Sky Sports: "We had a bid this week for Hamza, we rejected it. All was fine. Trained fine yesterday [Saturday], warmed up fine. I turned around to him at 60 minutes because I wanted two strikers on the pitch. Hamza told me he was injured.
"I don't know [if he refused to play.] I have to trust him but we'll see. The issue is that the transfer window is still open. There are a lot of people, one eye out the door and one in and we need people to be all in all the time in this football club.
"We really need that. At the minute there's still too many people uncertain or still trying to think, 'maybe there's something there for me'. The window needs to shut quickly.
"In-house we need to make sure that we have people who really want to be here, so the people that come in and the people that stay really want to be here. We'll see."
Boyd: Martin must be strong or he will pay the price
Following his former side's draw away to St Mirren, Sky Sports' Kris Boyd said:
"I think I said it a couple of weeks ago, I think the players have been running the club for far too long. Listen, if he's injured, he's injured. I highly doubt it.
"If that is the case, if I'm Rangers Football Club I'd drive him to the airport and say goodbye. If you've not got people who are willing to knuckle down and help this team at this moment of time, then see you later.
"If you don't there's a real danger. It's at boiling point right now with the fans. If Russell Martin is not strong, and doesn't see this through, he's going to join Giovanni van Bronckhorst, Michael Beale, Philippe Clement out the door.
"He needs to get the right type of characters in this dressing room and quick. I do question if Martin is a little too honest. After a game, emotions are still high and if you've turned to your bench for a striker that the fans think is the blue-eyed boy; I've not seen what everybody thinks.
"On a consistent basis, Hamza Igamane hasn't done what everyone thinks he's done for Rangers. He's another one who is inflated and everybody thinks is better than he is."
