Nakamura's future at Parkhead has been the subject of speculation amid rumoured interest from a number of European clubs.
And now Bologna, who gained promotion to Italy's top flight last season, have confirmed their intention to bring the 30-year-old back to Italy.
"We have already formalised our offer to Celtic, so they know the conditions of the proposed transfer.
"We are waiting to hear back from Celtic about the offer once they've discussed it with the player. We hope they'll give us permission to speak to Nakamura. If they do we'll contact him to discuss the move."