The one-time Manchester United trialist, 21, is refusing to sign a new contract in Florence as AC Milan continue to express an interest in securing his services, while Barclays Premier League club Liverpool are reportedly interested.
Ljajic, who scored 11 goals in Serie A last season, will start on the bench for Monday night's league game against Catania and Viola boss Montella revealed his decision was reached due to his frustration at the current impasse.
He told the Gazzetta dello Sport: "I'm fed up with this situation.
"Adem has felt he has a point to prove ever since the second half of last season, but it's also true that his colleagues and fans have stuck by him.
"He's received his coach's backing, too.
"I don't have the time or desire to keep waiting, especially because the lad is not happy.
"So from my point of view, a coach's point of view, I'm going to do things my way."
Montella insisted any disgruntlement aimed in his direction from fans over dropping the mercurial Serbian would fall on deaf ears.
He added: "I don't know what the fans will think but it's fair that everyone feels how they want to feel. That goes for both fans and the players.
"Boos and whistles do not have the power to influence clubs, or players."
Fiorentina's chief executive Sandro Mencucci, meanwhile, reiterated the club's view that Ljajic will be sold if he does not sign a new contract.
Mencucci said: "He won't remain here without renewing his contract. It won't be right.
"We have offered him a really good contract. If he considers it to be adequate, it will be good. Otherwise, he will leave.
"Should he stay with us, and I'm optimistic about this, we will be stronger on a technical level.
"Otherwise, we will sell him for an adequate sum. Also, there are many teams interested in him."