The Gunners made a dramatic last-ditch effort to sign the 21-year-old earlier today, tabling a £92m bid which would have smashed their previous transfer record.
Monaco are understood to have accepted that offer, but reports quickly emerged claiming that Arsenal had then pulled out of the deal as there was not enough time to complete it before the deadline.
However, the Evening Standard reports that Lemar was unwilling to join a Europa League club and prefers a move to Liverpool, who have also been credited with an interest.
The decision could mean that Arsenal refuse to sell Alexis Sanchez on deadline day, with the Chilean wanted by Manchester City.
Liverpool, meanwhile, have so far been unwilling to meet Monaco's valuation of Lemar.