The 36-year-old, who is available on a free transfer after leaving AC Milan, has been linked with a move to the Serie A outfit.
Negotiations have reportedly stalled in recent weeks, but according to Moreno Roggi, a deal is now close to being completed.
"We're just waiting for the call from Fiorentina. It is a destination that Massimo really likes and he isn't the only one, as you can tell by the interest from players like Mario Gomez and David Villa," Roggi told Lady Radio.
Ambrosini spent 18 years with Milan.