Lyon president Jean-Michel Aulas has told Arsenal they must sign Houssem Aouar by Friday or the deal is off.
Speculation has mounted in recent weeks suggesting the Gunners will make a move for the the French midfielder, who impressed in both Ligue 1 and the Champions League last season.
But Lyon are said to be holding out for a fee of around £55m, with Arsenal currently not willing to go above £32m.
The transfer window does not close until Monday, but speaking to Telefoot Aulas insisted he wanted all Lyon's business to be concluded by Friday.
"We will tell the players that whatever will not be settled in terms of departures before Friday, there will be no more departures," Aulas said.
"So for us the [closing] date of the transfer window will be Friday. I think I will propose it tomorrow (Tuesday) to Rudi Garcia and Juninho, because it's understandable.
"And all people of goodwill can see that there is something wrong (with the results of the team). It can be because of that but it can also be a lot of other things.
"In any case, from Friday, the players who have not left will not leave."
It remains to be seen if the two clubs can come to an agreement by Friday, but there is no doubt that Gunners supporters are desperate for the player to sign.
Aouar, who has spent his entire career at Lyon, was a big part of the side which made it to the Champions League semi-finals last season, but is now thought to be keen on a move to a major European league.
Another player who could leave Lyon by Friday is Memphis Depay, who has been strongly linked with a move to Barcelona to act as Luis Suarez's replacement.
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