The Viola boss is frustrated by the ongoing uncertainty surrounding the Serbia international's future at the Artemio Franchi
The 21-year-old, whose contract expires next summer, has been subject of intense speculation as of late, with AC Milan and Atletico Madrid among those reportedly poised to make a move for the wantaway star.
It is understood the Serbia international has been given a Tuesday deadline to decide whether or not he wishes to extend his stay at Stadio Artemio Franchi - but Montella has admitted that his patience is already wearing thin.
"I am fed up of the situation," the former Italy international told reporters ahead of the club's first game of the season against Catania, on Monday.
"I think he showed something in the second half of last season, proving that he appreciated the support shown to him by 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 not focused on his work."
The team's training session on Saturday was reportedly interrupted by a group of supporters, who proceeded to heckle Ljajic for his perceived reluctance to remain at the club.
Montella added: "The fans can do what they want to, just like Adem. I don’t think a few jeers can condition a player or a club. At times, jeers are a sign of interest ..."
Milan have already had an offer of around €8 million rejected by Fiorentina, with Viola vice-president Paolo Panerai taking to Twitter to label the offer as "unacceptable".
Ljajic has netted 16 times in 88 appearances during his three-year stay in Florence.