Milinkovic-Savic still has 18 months left on his Lazio contract, but Lotito is eager to have the 27-year-old put pen to paper on a new agreement.
"Contracts are done when they expire. From a technical point of view we have an interest in renewing him because he is a great player and a great man, I hope that the player will do the same," said Lotito after receiving the Colalucci award.
"Milinkovic-Savic is a player Lazio are banking on, he is an added value.
"What's missing are presidents, we have no problem finding players or coaches. There are only a few Italians left who do it with dedication. Money is not everything in life, ideas count."
Meanwhile, Juventus are under investigation by the Turin Public Prosecutor's Office after allegedly paying their players in secret during the early stages of the COVID pandemic, even though they had publicly stated that the wages were waived.
This development has led to widespread criticism of the Old Lady, but Lotito came to Juve's defence.
"Today everyone speaks badly of Juve, but they have contributed to the livelihood of Italian football.
"To say that Juve are the evil of Italian football is unfair. Today everyone goes out of their way to create dissent against Juventus."