Highly-rated Serbian Ljajic, 21, has also reportedly attracted the attention of Premier League sides such as Manchester City this summer.
But it is Milan who are understood to be leading the chase and Ljajic's representative is keen to hold talks about the situation, with there just one year left to run on his client's contract.
While Ljajic would like to extend his deal, he accepts that it is up to Fiorentina to decide on his future.
Agent Alex Vaiata told milannews.it: "We know of AC Milan's interest, even if they have not contacted Adem.
"They talked directly to Fiorentina and it's up to the two clubs to decide and try and reach an agreement.
"There has been no negotiation about a new contract because the player was not in Florence, but now there will be a way to talk with Fiorentina and we'll see if there is a chance to extend.
"However, if they decided to sell him at Milan, we will consider this hypothesis."