Arsenal target Nicolas Pepe is also weighing an offer from Napoli and will decide his future at the start of the coming week, a source close to the deal told AFP on Sunday.
A second source said French champions Paris-Saint Germain had also entered the race to sign the 24-year-old.
The Ivory Coast striker, who featured on five occasions for his country at the African Cup of Nations, scored 22 goals last season as Lille finished in a surprising second place in Ligue 1.
British media reported on Sunday the Gunners had scheduled a medical for Pepe.
The first source told AFP it was not certain the 13-time international would end up in North London.
“The club have received three written offers for 80 million euros ($100 million) and the player will probably choose either Arsenal or Napoli,” the source said.
“This should be settled by Tuesday,” the source added.
“Both clubs are offering him a net salary of 8 million euros a year.
“Pepe’s preference would be for Arsenal, who will be competing in the Europa League this season. But the prospect of playing in the Champions League with Napoli and coach Carlo Ancelotti could still turn the balance to Italy.”
The second source said PSG were also interested in the Paris-born forward but their approach may have come too late and could also be hampered by their need to trim costs to satisfy UEFA’s financial fair play rules.
Contacted by AFP, Lille president Gerard Lopez refused to comment.