Lemar was linked to Liverpool and Arsenal in the summer but remained on the French Riviera after former team-mates Kylian Mbappe, Bernardo Silva, Benjamin Mendy and Tiemoue Bakayoko all left for pastures new.
But Jardim admits a big offer this month could mean Lemar makes a move to the Premier League before the current campaign is over.
In Liverpool's case, the British record deal to sell Coutinho to Barcelona has seemingly set a precedent, and Monaco are said to be of the belief that "Lemar's value has also risen".
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.More news: British PM May to reshuffle cabinet, appoint new ministers
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"Monaco's position is that they don't intend to sell any of their top players this month".
And according to the Mirror, Monaco would be seeking an eye-watering fee of at least £90 million if they were to sell the 22-year-old.
"And then going to Liverpool where, okay, like I say it's great but you might not play much and when you play you might be gapped because you will need a little bit of time to adapt to the league and to the culture and to the language and everything, six months before a World Cup, so it's just not a given. But I can see why Liverpool want it to happen now as well".