The 30-year-old, who is rumoured to be a target of both Arsene Wenger and Martin O'Neill, has been with the Florence-based side since 2006.
Fiorentina recently completed the signing of former Celtic stopper Artur Boruc, throwing Frey’s future into doubt.
However, Frey’s agent has insisted that the stopper is not bound for either Villa Park or Emirates Stadium and instead is happy to remain in Italy and fight for his place.
"Aston Villa have never spoken with Fiorentina. I think lots of people have fun saying rumours," Branchini told Violanews.com.
"Frey will stay in Florence regardless of everything and everyone. I think he has also shown his love for the city and Fiorentina."
Arsenal manager Arsene Wenger has been linked with a string of goalkeepers this summer following the inconsistent form of both Manuel Almunia and Lukasz Fabianski.
The agent of Slovenia and Udinese goalkeeper Samir Handonovic recently denied reports that the Gunners had made an approach for the highly-rated custodian.
Aston Villa could be in the market for a new gloveman with first choice Brad Friedel nearing his 40th birthday.
Villa manager Martin O'Neill signed American international Brad Guzan with the intention of him being Friedel's long-term replacement.
However, it is thought he does not believe Guzan is currently up to the task.
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