The Morocco international joined the Gunners on a Bosman free transfer from Bordeaux in 2010 but has failed to hold down a regular place at the Emirates Stadium.
Arsenal boss Arsene Wenger was this week quoted as saying Fiorentina had made an offer for the 28-year-old but Viola sporting director Daniele Prade dismissed that claim and cited the player's wages as one reason they would not be pursuing a deal.
Prade told SportItalia: "Have we made an offer for Chamakh? We have not made one because he earns three million euros (per season)."
Prade did confirm, however, that Chamakh's Morocco striker partner Mounir El Hamdaoui would soon join the Florence outfit from Ajax.
"We hope to complete El Hamdaoui's transfer tomorrow [Wednesday]," Prade said. "He is a striker that our coach (Vincenzo Montella) likes a lot."
Prade also announced the club would only consider selling leading striker Stevan Jovetic this summer if they receive an offer above 30 million euros.
Jovetic has been strongly linked with a move with reports in Italy claiming that Chelsea, Arsenal, Liverpool and Juventus are all in the race to acquire the Montenegro international.
Fiorentina are, however, reluctant to sell the 22-year-old, who is under contract with the Tuscan outfit until June 2016.
"Since the start of the season we have said that we are not selling Jovetic," Prade said. "There is, however, an agreement with the player that (should we get an offer) above a certain figure, we will sit down and evaluate the offer.
"So far we have not received an offer for the player.
"He is a top player and we will only consider offers above 30million euros."