The Monaco star enjoyed a staggering breakthrough playing under Leonardo Jardim at the Stade Louis II last season.
And his performances as they marched to the Ligue 1 title have seen him emerge as one of Arsene Wenger’s top targets.
French outlet Le 10 Sport claim Arsenal have made a series of bids for Lemar - coming in at €40m [£35.7m], €45m [£40.2m] and €50m [£44.7m].
However, Monaco are determined to keep hold of the 21-year-old having already lost midfielders Tiemoue Bakayoko and Bernardo Silva this summer.
It seems the French champions may have to fight off interest from Liverpool too if they’re to ensure they retain Lemar though.
Le 10 Sport reckon Jurgen Klopp is seriously considering the midfielder to replace Barcelona target Philippe Coutinho.
The Brazilian has been tipped to swap Anfield for the Nou Camp if Neymar quits the La Liga giants for Paris St-Germain.
And with that pair of deals potentially moving closer, Le 10 Sport say Liverpool are weighing up their options.
The French outlet indicate the Reds are yet to reach out to Monaco or Lemar’s representatives regarding a switch.
But they reckon Liverpool will be in touch once Neymar and, more importantly, Coutinho’s futures are sorted out.
Arsenal may have an advantage over Klopp though, with Lemar apparently hoping to move to the Emirates.
