Vlahovic has been heavily linked with a move away from La Viola this month, with a host of Europe's top clubs thought to be interested in the 21-year-old.
However, Barone has now called on Vlahovic to address the speculation surrounding a possible exit this month rather than allow the rumours to continue growing.
"There is talk about Dusan Vlahovic every day now. We just want to talk about the squad. We've already said so much about him, we expect a response from him and his entourage on what the future holds," Barone told Sport Mediaset.
"We have our plans and we are activating those immediately. I had a long conversation with Dusan the other day and I told him we need to understand his path. If he wants to stay at Fiorentina, then sign the contract. If he wants to leave, then say so publicly.
"He can't string an entire club, city and fanbase along waiting for him. From what I heard, he is not prepared to speak out, so we have to make our decision within the club.
"Of course, we are ready to evaluate anything that arrives. So far, no offers have arrived."
Vlahovic has scored 19 goals and created three more in 23 appearances for Fiorentina across all competitions this season.