Arsenal attempted to sign Lemar last summer, failing with a bid late in the transfer window, and remain keen on the France global, while Liverpool have been linked following the sale of Philippe Coutinho.
Lemar is regarded as one of the most exciting young midfielders to have emerged out of France in recent years, thanks largely due to his exploits for Monaco last season.
That development will be welcomed by Arsenal if Arsene Wenger does decide to push forward with a move for Lemar.
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Both Liverpool and Arsenal were close to a deal on deadline day during the summer with the Gunners even making a £90 million bid for the attacker.
All the latest Arsenal transfer news and rumours from across the British and European press on Tuesday, January 9.
Jardim has made it clear on several occasions that he doesn't want to sell Lemar although the manager knows anything can happen when it comes to the January transfer window.
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Only last week, Jardim gave a much more conclusive answer when quizzed on the chances of Monaco's big players leaving this month, per Jack Rosser of the Evening Standard: "We are not in the habit of doing major sales of players (in the winter transfer window)".
The Mirror says Liverpool will now intensify efforts to bring Lemar from Monaco.
According to the Sun, Liverpool are set to swoop for the £90million rated ($121.9million) star by readying an offer for him this month.
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