The veteran striker's contract with Major League Soccer outfit LA Galaxy ends at the end of the year, while the season has already concluded for the player after a playoff loss to Los Angeles FC.
Ibrahimovic has hinted at a return to the Italian top flight, with Napoli reportedly keen on the striker's services while Manchester United's name has also popped up a possible destination.
However, Bologna director Walter Sabatini claims the 38-year-old wants to join them due to his relationship Sinisa Mihajlovic.
"Ibrahimovic wants to join us because of his rapport with Sinisa," the director told TuttoMercatoWeb, according to Football Italia.
"It's not impossible. It can be done, but if it is, it'll be because of the affection that bonds them together.
"Ibra would like to help Mihajlovic and I can say we'll do everything to make this madness happen."