The Rosanero lost 1-0 Fiorentina on Sunday to seal their demotion to Italy's second tier after nine seasons in Serie A.
Their relegation has placed the futures of a number of star players in doubt, most notably Slovenia defender Ilicic.
The 25-year-old has impressed since signing from Maribor in 2010 and the club reportedly had to fend off interest from AC Milan, Tottenham and Liverpool during the last two transfer windows.
However, following their relegation president Zamparini admits they will struggle to keep hold of the player this summer should rival clubs renew their interest in him.
"Josip Ilicic is a player for big clubs so I really doubt that he will stay with us," he said. "We will have to talk of course but he has already told me that he will leave if he gets an offer from a big club. And I don't doubt that he will get one."
Ilicic's representative Amir Ruznic believes AC Milan have been tracking the defender and expects them to ramp up their interest in the summer.
"There have been no talks and nobody has called me from AC Milan," he told Milan News. "But it would not surprise me if AC Milan thought of him. It is normal that a player like Ilicic pleases a club like AC Milan.
"But the season is not over yet and there will be enough time to speak about that later."