Ivanovic is yet to make a single appearance for the Blues since joining from Lokomotiv Moscow in a £10million deal in January.
Whether that transfer will be permanent or a loan move remains unclear, but Borozan warned that the player was unhappy to be a back-up in west London and that he had set his heart on a move to the north of Italy.
"Branislav chose Milan and he told that to the club, and for that reason he will probably wear the Rossoneri shirt this next season," he told tuttomercato.com.
"The deal will be done because no-one will keep an unhappy player."
Despite suggesting a deal was imminent, Borozan conceded negotiations between the clubs had stalled because of Chelsea's reluctance to let the defender leave Stamford Bridge.
Only last week Borozan revealed Chelsea had refused to sell the player because they regarded him as an "indispensable" member of the team.
"The problem at the moment is that Chelsea want four starters in the position and he is the fourth. It's difficult to find a replacement of the same level, so the Blues want to keep him and the deal has stalled," Borozan said.
"The English are bringing grist to their own mill to up the price a bit."