The Gunners have tracked Lemar throughout the summer but Arsene Wenger appeared to have admitted defeat last week.
However, Liverpool entered the race for Lemar and Monaco have since softened their stance on keeping the French international to give the Gunners hope.
Alexis Sanchez is desperate to complete a deadline day move to Manchester City but Wenger knows he needs a replacement before the Chilean can be allowed to depart.
The Gunners are happy to let Sanchez leave should they find a top replacement and the Independent report that Monaco have accepted Arsenal’s £92million bid for Lemar.
However, the 21-year-old is said to favour a move to Anfield and could wait until the dying hours of the window to see if Jurgen Klopp’s side match Arsenal’s offer.
Regardless, it’s a strong sign of intent from the Gunners to break the British transfer record – which Manchester United currently hold for their £89m outlay on Paul Pogba in 2016.