The 30-year-old has been identified as a potential signing by Gunners boss Arsene Wenger as he searches for a new number one, but it was thought Frey was happy to stay in Florence where he is under contract until 2013.
However, he has now admitted he may be ready for a new challenge and is believed to be keen on testing himself in the Premier League following a disappointing campaign with Fiorentina, who finished 11th in Serie A.
Frey told Gazzetta dello Sport: "I have spoken to (Fiorentina president Diego) Della Valle.
"I will speak again with him after the holidays.
"In life, at times, you need new challenges and I cannot hide the fact that I need that.
"Perhaps finding new challenges doesn't necessarily mean leaving, it could also mean that I could stay provided the team is reinforced."
He added: "Next season we will not play in Europe and that is why we need a strong team to be at the highest level in Serie A."
Manchester United have also been linked with the Frenchman, who is valued at around £8million by Fiorentina.
Meanwhile, reports suggest Wenger is also monitoring Robert Green's situation at West Ham and the Frenchman may be tempted to make a bid for the England man as he weighs up his summer transfer options.