Alfredo Morelos is reported to have asked Rangers to accept a bid of around £18m from Lille.
Manager Steven Gerrard left Morelos out of his squad for Saturday's 2-0 win against Kilmarnock at Ibrox after saying that he was “disappointed the player has had his head turned and doesn’t look himself".
The 24-year-old has scored 79 goals in 142 games since being brought to Ibrox by Pedro Caixinha in 2017.
Colombia-based WinSports journalist Pipe Sierra has this afternoon tweeted: "CONFIRMED: Colombian forward Alfredo Morelos (24) has formally requested the #Rangers to accept the 20M offer € made by him by #Lille."
He added that these were "decisive hours".
Speaking after that victory over Kilmarnock, Gerrard explained his decision not to include Morelos.
He said: “If I see people who have taken their eye off the ball and are not really hungry to get this football club results, I have to make decisions and Alfredo made it easy for me.”
24 clubs have been mentioned in connection with the striker, with Ligue 1 side Lille having already had a bid rejected.