Newcastle have been busy bolstering their French contingent during the January transfer window and have held a long-standing interest in Thauvin.
The France youth international, who turned 20 on Saturday, has 18 months left on his contract and Bastia say he does not intend to sign an extension.
Geronimi has stated that Newcastle are the only club to have made an offer for Thauvin, but that Arsenal manager Arsene Wenger has been in contact about the player.
"Florian Thauvin has been the object of just one concrete offer so far, from Newcastle, for €3million (£2.6m), but we refused it," Geronimi told France Bleu radio station.
"However, he didn't want to prolong his contract with Bastia, but he will stay until the end of the season."
Regarding Arsenal's interest, Geronimi added: "We have not received any firm offer from Arsenal and, thus, there is no question of the €5m (£4.3m) reported.
"This week I have had Arsene Wenger on the phone twice. He expressed his interest in the player to us, but it has not gone beyond that."