Ibrahimovic this week confirmed his departure from LA Galaxy after two seasons in Major League Soccer (MLS).
The 38-year-old intends to see out his career in Italy, Galaxy head coach Guillermo Barros Schelotto claimed, and will not be short on options given his free agent status.
AC Milan, Fiorentina and Napoli are among those to have been linked but Bologna could have the inside running thanks to Ibrahimovic's rapport with Rossoblu boss Sinisa Mihajlovic, who crossed paths with the Swede at Inter Milan.
"There is a month and a half to go until to the transfer window opens," Bigon said.
"As has been said, Ibrahimovic and the coach have a strong personal relationship.
"He expressed an openness to the idea of coming to Bologna but now he will take time, after announcing the farewell to MLS, to evaluate all the possibilities for his future.
"We are very fascinated by this situation but it is clear that we do not control it 100 per cent.
"The choice is exclusively down to the player. We will wait in case [Ibrahimovic confirms his interest], then we will be ready and more than positive."