Milan sports chief Igli Tare stated earlier this week that an offer is in front of Modric, 40, something Allegri has now affirmed.
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The coach stated: "We haven't discussed it yet. It's Luka's decision, and we're waiting for his answer.
"Luka has contributed his technical skills, but above all his human and professional qualities, to the entire environment and the team, especially the younger players.
"Seeing a 40-year-old man with this passion is incredible, and it generates enthusiasm."