The Sky Sports News reporter has claimed that the north London side are still keen on bringing the 21-year-old midfielder to The Emirates this summer from the Ligue 1 side.
There had been reports over the weekend that the Gunners had tabled a fresh bid for the attacking midfielder as Arsene Wenger searches for his third signing this summer.
However, Sheth has claiming that the Gunners have actually only had two bids turned down for the player, the latest of which was worth around £40m.
Speaking on Sky Sports News on Tuesday evening, Sheth said: “It still could be a pretty busy time at Arsenal with regards to big-name arrivals at The Emirates.
“We’ve talked about so many players who could potentially be leaving Arsenal, but the name Thomas Lemar will not go away.
“Arsenal remain interested in the Monaco winger, despite Monaco insisting that the player is not for sale. Arsenal have had two bids rejected already, the latest being £40m.”
Arsenal have signed just Sead Kolasinac and Alexandre Lacazette this summer as Wenger prepares his team for the new season.
The north Londoners finished in fifth place in the Premier League last term but still ended the campaign with a trophy when they beat Chelsea to win the FA Cup.
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