Fred has given himself a 50-50 chance of staying at Lyon beyond the end of the January transfer window.
The Brazil striker recently signalled his intention to leave Les Gones after losing his place in the starting line-up to Karim Benzema.
Paris St Germain and a host of English clubs, including Manchester City and Middlesbrough, have been linked with the 24-year-old.
He has not completely discounted remaining at the Stade Gerland, however.
"I am now at the disposal of the club and the coach (Alain Perrin)," said Fred, who only returned to training following the winter break on Wednesday, a week and a half after his team-mates.
"I want to get back to normal with the aim of playing for OL.
"At the same time, if an offer comes, an offer which is good for me and the club in the form of a definite transfer, not a loan, I will leave.
"It is 50-50. But I have a year and a half left on my contract. If I stay at OL, I am going to give everything for the club."
Fred revealed he had received "two or three offers which did not interest me and which I refused".
But he said PSG, who have been strongly linked with a move for the Brazilian, have yet to make a bid.
Paris St Germain and a host of English clubs, including Manchester City and Middlesbrough, have been linked with the 24-year-old.
He has not completely discounted remaining at the Stade Gerland, however.
"I am now at the disposal of the club and the coach (Alain Perrin)," said Fred, who only returned to training following the winter break on Wednesday, a week and a half after his team-mates.
"I want to get back to normal with the aim of playing for OL.
"At the same time, if an offer comes, an offer which is good for me and the club in the form of a definite transfer, not a loan, I will leave.
"It is 50-50. But I have a year and a half left on my contract. If I stay at OL, I am going to give everything for the club."
Fred revealed he had received "two or three offers which did not interest me and which I refused".
But he said PSG, who have been strongly linked with a move for the Brazilian, have yet to make a bid.
Copyright (c) Press Association
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