The Gunners launched a £90m (€100m) bid to try and sign 22-year-old Lemar on the final day of the summer transfer window as they looked to bring in a replacement for Alexis Sanchez, who was then on the brink of joining Manchester City.
That followed two bids from Liverpool during a frenetic final week of the window, one of which was said to have been worth €90m lodged 48 hours before the window closed. Such was their level of interest, the Reds' medical team was reportedly left on standby during that time to travel to Paris – where Lemar was based with the France national team – to carry out a medical if a deal was struck.
Monaco vice-president Vadim Vasilyev later confirmed interest from both sides – adding Arsenal were the closest to clinching a deal – and admitted a move away from the Stade Louis II for Lemar star will surely beckon next summer.
The club did not rule out the possibility of a January exit however with L'Equipe now reporting both Arsenal and Liverpool will renew their efforts to sign the player next month.
But the report adds however Lemar has a new suitor in Premier League champions Chelsea, who have made contact with the Frenchman's representatives in recent weeks to make their interest known.
The Daily Telegraph adds Antonio Conte's side will have the added advantage of being able to offer players on loan to sweeten a deal for the attacking midfielder. Michael Emenalo, who last month left his role as technical director at Stamford Bridge, has since taken up a similar position at Monaco, a switch Chelsea believes could aid their pursuit of the player.
Lemar, who was also linked with a move to Barcelona last summer, was instrumental in Monaco's Ligue 1-winning campaign last season, scoring 14 goals and laying on 17 assists in all competitions.
But in the wake of a lengthy summer transfer saga, his form has suffered, scoring just once and providing three in 15 appearances, with Monaco's Champions League campaign over for Christmas and the club nine points adrift of Paris Saint-Germain in the French top flight.