The 40-year-old joined the Italian club on a free transfer last summer after leaving Real Madrid, where he spent 13 seasons.
His one-year deal includes an option for a second year that is triggered by the player himself, not the club — an unusual arrangement that reflects his standing within the squad.
Modrić's first requirement is Champions League football. Milan are currently third in Serie A, though their recent form has been patchy — just two wins from their last five league games — and teams as low as sixth remain in contention for the European spots. The second condition is that Massimiliano Allegri remains as head coach.
The Italian has played Modrić in almost every league game this season and built his system around the Croatian's intelligence and positioning. The third is a broader assurance that Milan will be competitive on all fronts next season.
Modrić turns 41 in September and will also represent Croatia at the World Cup this summer before making his decision. The club, the coaching staff and his teammates are all pushing for him to stay, with his impact on the dressing room cited as much as his ability on the pitch.
Meanwhile, Calciomercato reports that Milan are approaching an agreement to sign Mario Gila from Lazio. The 25-year-old Spanish centre-back is contracted until 2027, with Lazio reported to be seeking around €25 million for his signature.