Lyon do not expect to beat Paris Saint Germain to the signing of Jeremy Clement.
The Rangers midfielder is expected to return to France during the transfer window after just six months at Ibrox.
Former Gers boss Paul Le Guen, now in charge of PSG, is keen to sign the young Frenchman, while previous employers Lyon hoped to bring him back to Stade Gerland.
But the French champions have now given up on their attempts to sign Clement, despite agreeing a fee with Rangers.
Chairman Jean-Michel Aulas will pursue other targets in a bid to land a defensive midfielder before the end of the month.
"We are at a dead point with Jeremy Clement, because we quickly found an agreement with Rangers, but the Paris coach explained to him he would play every match with them and wouldn't play much with Lyon," Aulas told AFP.
"If I was a defensive midfielder in Paris, I would worry.
"We have to wait for Clement's decision, but as we have a number of other alternatives, we haven't waited for his response, even if we have agreed terms with the Scottish club.
"We haven't got a priority, Gerard Houllier has just asked for a defensive midfielder.
"Something could happen before January 31st."