The Gunners have had three bids knocked back for Lemar, 21, who is Arsene Wenger's top transfer target.
French newspaper l'Equipe say the latest one topped £44.7m but Monaco are adamant they're not selling.
They've already seen the bulk of their big-name players leave and are worried Kylian Mbappe could join the exodus.
He is being lined up by Real Madrid and Monaco chiefs are desperate to avoid any more of their star men going.
Speaking on Sky Sports' Transfer Centre show, Sheth said: "Despite Monaco's insistence that he stays at the club, we understand Arsenal maintain a keen interest in the player.
"It's thought talks between the clubs continue.
"Monaco's not for sale stance has been seen in some quarters as a way to encourage Arsenal to make a higher offer.
"Perhaps we haven't heard the last of Thomas Lemar in this window."
