The Serbian's contract expires next June and the Serie A club have been unable to get him to sign fresh terms.
He has until Tuesday to put pen to paper or find a new club but has been included in the squad for Monday's visit of Catania.
Montella, however, appears to have lost his patience.
"I'm fed up of this situation," he said. "I think he showed something in the second half of last season, receiving in return the support of his team-mates, club and coach.
"I have neither the time nor the desire to wait for him, seeing as he's not calm and focused on his work."
Disgruntled supporters made their feelings clear when they staged a protest during Saturday's training session, but Montella doubts whether it will have any impact.
"The fans can do what they want to, just like Adem," he added. "I don't think a few jeers can condition a player or a club. At times, jeers are a sign of interest."
Looking ahead to Monday's game, the Italian added: "Catania are a very strong side and have hardly changed since last season, so they are a solid unit.
"We won't rest players ahead of the Europa League play-off with Grasshoppers. We'll use the players most functional to this match."
