The Sky Sports News reporter is claiming that the two clubs are still in discussions about the possibility of the 21-year-old attacking midfielder moving to The Emirates, despite no deal yet having been agreed.
Arsenal have long been linked with a bid to try and bring Lemar to north London this summer as Arsene Wenger looks to strengthen his attacking options ahead of next season.
Reporter Sheth claims that Arsenal have already had two bids for the midfielder rejected, but that has not put the Gunners off in their search to make him their third signing.
Speaking on Sky Sports News on Wednesday evening, Sheth said: “Another story that refuses to go away despite one club’s insistence that the player will not be sold is Monaco winger Thomas Lemar.
“Arsenal remain interested and it is my information that dialogue continues between the clubs.
“Monaco said last week that Lemar is central to their plans and have rejected two bids from Arsenal already.
“It is thought Arsenal may need to break their transfer record again to have any chance of signing Lemar.”
Arsenal have signed two players so far this summer after having wrapped up deals to land Alexandre Lacazette and Sead Kolasinac.
The north London side are preparing to take on Chelsea in the Community Shield at Wembley on Sunday as they look to win the first piece of silverware on offer this season.
The Gunners finished in fifth place in the table last term but won the FA Cup for the third time in four years.
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