The Croatian’s previous deal with the Rossoneri expired on June 30, but talks have progressed positively in recent weeks.
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The 40-year-old had been focused on Croatia’s 2026 World Cup campaign before turning his attention back to his club future.
According to Sky Sport Italia, the efforts of Milan’s directors and new head coach Ruben Amorim have played a key role in convincing Modric to continue at San Siro.
Modric, who has long admired Milan, is reportedly leaning towards accepting the offer and could join the squad during their pre-season tour of Australia, which begins on July 26.