The former Juventus ace is unsure of his future at The Artemio Franchi as he is still to be convinced by the club's ambitions.
The 35-year-old has experienced a troubled time in Florence this season with the side struggling at the wrong end of the table and the cash-strapped club unable to pay the players` wages during part of the campaign.
Di Livio is more than willing to stay even if they do as expected suffer relegation to Serie B, but he wants to be assured of the club's future plans.
"I'm ready to remain here if the club can prove to me that they have a project which will see us immediately win promotion back to Serie A," said Di Livio.
"But seeing what has happened in the past few weeks and now that President Ugo Poggi is set to quit, I'm seriously reflecting on my own future."
