A bid of £2.6m was rejected for the 19-year-old, who is also attracting interest from Arsenal.
Newcastle have held a long-standing interest in the highly-rated youngster, although Geronimi has revealed that he has personally spoken with Gunners manager Arsene Wenger regarding Thauvin's future.
"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.
"However, he didn't want to prolong his contract with Bastia but he will stay until the end of the season."
"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."
Thauvin joined Bastia from Grenoble in 2010.