Montella is keen for the matter to be dealt with as soon as possible and the club have given the 21-year-old attacking midfielder until August 27 to make a decision on his future.
"I am fed up of the situation," Montella told reporters.
"I think he showed something in the second half of last season, proving that he appreciated the support shown to him by his teammates, 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."
Ljajic made 31 appearances for La Viola last season, scoring 12 goals.