Lyon president Jean-Michel Aulas believes Fred could still leave in the January transfer window, despite the striker announcing he will be staying at the club.
The Brazil international confirmed on Thursday he would be remaining at the Stade Gerland despite interest from Paris St Germain, Tottenham, Middlesbrough and Portsmouth.
But Aulas, who had been prepared to let the 24-year-old leave, insists it may not be the end of the transfer saga.
"He is going to play the waiting game until January 31, and perhaps after that," he said.
"He has just announced that he is staying? That's great. But he can also say the day after tomorrow that he is leaving for Tottenham or Middlesbrough because they gave him what he wants.
"What bothers me most is his indecision. If I knew that he said this because he really wanted to stay, I would be relieved."
Fred had been keen to leave Les Gones after losing his place in the first team to the in-form Karim Benzema.