The 32-year-old striker is looking for a new club after terminating his contract with Parma last week over a wage dispute.
"We are doing all that we can," Bari president Gianluca Paparesta told Gazzetta dello Sport. "Cassano has several days left to decide.
"Cassano has to make a life choice and he is considering the offer.
"Bari is not like any other city and, for him and for his family, it would mean more tension and less freedom of movement than other places."
Cassano began his career with Bari and went on to play for Roma, Real Madrid, Sampdoria, AC Milan and Inter Milan.
The former Italy international scored five goals and set up two more in 19 league appearances for Parma this season.
Bari was declared bankrupt last year before a consortium led by Paparesta acquired the Apulia club.
It is 14th in Serie B with eight wins in 24 league games.
