The 27-year-old forward wants to leave the Giallorossi outfit this summer and has been strongly linked with a move to Juventus in recent months, while Tottenham and Blackburn Rovers have also been mentioned as possible suitors.
"It's Vucinic that wants to leave," said Roma sporting director Walter Sabatini. "If it was up to us, he could stay.
"We have granted him (Vucinic) his wish to listen to eventual offers that arrive but Juve has not stepped forward so far.
"I can say that until tomorrow afternoon, Vucinic's price will be the same as it is now, but after that he will cost more."