Ljajic is reportedly a long-term target for domestic rivals Milan and has yet to sign a new contract with Fiorentina, with his current deal set to expire in July 2014.
The Serbian was an integral part of Vincenzo Montella's side last season, scoring 12 goals in 31 appearances as Fiorentina narrowly missed out on qualification for the UEFA Champions League, Milan securing third place in Serie A on the final day.
Fiorentina play their first competitive game of the new season when they take on Swiss side Grasshoppers in the first leg of the UEFA Europa League play-off round on Thursday.
Montella's men head into the clash with Ljajic's future still to be decided, but Mencucci is confident a resolution will be reached.
"We're near the end of the market and are nearing the end of the story," he told Corriere dello Sport.
"All possibilities are open. I am always optimistic and I'd like to see this deal being resolved for the best."
Montella, who has boosted his forward line in the off-season with the signing of Mario Gomez from Bayern Munich, admits the constant speculation over Ljajic could have an impact on the 21-year-old.
"I see him looking relaxed, even if being young it’s inevitable he could be affected by all this," Montella said.
Fiorentina start their Serie A campaign on Monday when they host Catania at the Stadio Artemio Franchi.
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