The Gunners are facing a battle to keep their big-name players Mesut Ozil and Alexis Sanchez in the January transfer window.
Both Ozil and Sanchez have been linked with a potential switch to Manchester United this month given their current contract situations.
The Chile international has also been touted with a move to Premier League leaders Manchester City following his failed summer move.
Arsenal attempted to sign Lemar in a £92m deal last summer but the attacker turned down a move to the Emirates Stadium.
The Gunners will have a big void to fill should either Ozil or Sanchez leave, opening up the possibility of Arsenal relaunching their Lemar bid.
Sky Sports News reporter Sheth confirmed that Arsenal do have a long-standing interest in the Monaco forward but ruled out Lemar leaving his current employers this month.
“They have had a long standing interest in Lemar,” Sheth told the Transfer Talk podcast. “[But] Monaco won’t be selling him in January.
“The likelihood is he will be leaving in the summer.”
Lemar scored 11 goals and made 12 assists in 48 appearances in all competitions last term as Monaco won the Ligue 1 title and reached the Champions League last four.
Arsenal haven’t won the Premier League title since 2003-04, while the Gunners finished in sixth spot in the Premier League table last term.
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