Jean-Michel Aulas said on Twitter that there was not enough time left to find a replacement for the France forward, who is in the final year of his contract with the club, and hence Gomis would not be sold.
Aulas said the club didn't want Gomis to reach the end of his contract and leave on a free transfer.
"We have to face facts, there isn't an offer that Bafe has accepted despite (interest from) the 'English' and the 'Turks' and Lyon need a player like him," he tweeted.
Gomis, who was deemed surplus to requirements at the end of last season, has been kept apart from the first team squad for having refused either to sign a new contract or join another club.
The transfer window is due to close on Monday at midnight.
Lyon lost 2-1 at Evian on Saturday to leave them with six points from four matches and temporarily seventh, although they will drop down at least one place following Sunday's matches.
Bafetimbi Gomis to stay at Lyon, says president Aulas
Advertisement