The defender's current agreement runs until 2028, but Lazio president Claudio Lotito has decided to open discussions over improved terms after the 23-year-old established himself as an important part of Gennaro Gattuso's team.
According to Il Messaggero, talks began with a meeting between the two sides, with Lazio prepared to redirect some of the money freed up by the departure of Patric's final year of salary towards Floriani Mussolini's new deal.
The move represents a significant change in the player's position at the club.
Floriani Mussolini had been expected to leave Lazio during the summer, with Empoli having already reached an agreement for his transfer. Instead, Gattuso pushed for the club to keep him and the decision has since been rewarded by the midfielder's performances.
The Italy Under-21 international had endured a difficult moment earlier in the season when he conceded a penalty against Venezia. Gattuso viewed the incident as a mistake that came with experience and remained convinced that the player could develop into an important member of his squad.
Rather than allowing the setback to influence Lazio's plans, the coach persuaded the club not to proceed with the transfer.
Floriani Mussolini has responded by becoming a regular starter and demonstrating the application that convinced Gattuso to keep him.
There is still work to do. The Lazio coaching staff believe the player has areas of his game that require improvement, but his attitude has strengthened the belief that he can continue progressing.
That development is now being reflected in the club's contract strategy.
Lazio's decision to begin renewal talks is an indication that Floriani Mussolini's role has changed since the summer. What appeared to be a player on his way out has instead become someone the club wants to protect for the future.
Gattuso has been particularly important to that change.
The Lazio coach saw beyond the penalty conceded at Venezia and the uncertainty surrounding the player's place in the squad. His intervention effectively gave Floriani Mussolini another opportunity to demonstrate that he belonged at the club.
The defender has taken it.
With Lazio now looking to negotiate a new agreement despite the existing contract running until 2028, the club is seeking to reflect his increased importance and prevent another summer in which his future becomes uncertain.