The 19-year-old, who has been tipped as a star of the future, has reportedly been the topic of discussions between the French side and the Gunners, as Arsene Wenger looks to bolster his squad during the current transfer window.
However, Bastia have rejected the idea that the player could leave the club this month.
The statement read: "Sporting Club de Bastia categorically denies the discussions with Arsenal about Florian Thauvin.
"The club does not intend to participate in gossip and fantasies regarding the player moving for completely disproportionate transfer amounts, given the situation of the player and the current prices in the transfer market."
Arsenal are yet to sign a player during the January transfer window.