The offer is worth an initial £66m with £7.5m in add-ons.
‘Sky Sports’ has confirmed that Liverpool have made a bid, but at a much lower £55.5m.
Lemar, who has been the subject of three bids from Arsenal this summer, is reportedly keen on a move to the Premier League.
The Gunners final offer was worth £50m but Arsene Wenger confirmed last week that a deal was ‘dead’ after Monaco ‘closed the door’ on his departure.
Liverpool’s bid is almost £25m more than Arsenal’s valuation of the Frenchman and the huge figure could tempt the French Champions to sell.
A deal for Lemar would smash the Red’s current record transfer fee, which was broken this summer with £39m for Mohamed Salah.
The arrival of Lemar at Anfield would cause further tension among the Arsenal faithful with Wenger admitting defeat in the club’s pursuit of the 21-year-old days before the shocking 4-0 loss to Liverpool.
While Jurgen Klopp would have an extremely talented youngster at his disposal, any deal could could be a sign that Philippe Coutinho is on his way to Barcelona.
The Brazilian remains a target for the Spanish giants, despite a long and drawn-out transfer saga.
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