The 36-year old is available on a free transfer after his contract at the San Siro expired this summer, bringing an end to his 18-year spell with the Italian giants.
It was reported that Premier League side West Ham were also chasing Ambrosini's signature, but Roggi says that Fiorentina are leading the way having been in contact with their sports director.
"I spoke by telephone with Daniele Prade and we took a step forward with Fiorentina," he told Radio Blu Toscana.
"At the moment everything is suspended - there is no agreement yet but there has been an important approach between the two parties.
"We'll be in touch in a few days, I am optimistic."
Meanwhile, Fiorentina have completed the signing of goalkeeper Gustavo Munua from Levante who joins on a free transfer, as announced by the club on their official website.
"Fiorentina can announce that we have signed the player Gustavo Adolfo Munua Vera, who last season played for Levante UD," a statement read.
"He has signed a contract that binds him to the Viola until June 30, 2015."