As revealed by Goal.com earlier this month, the former Sampdoria star is keen on a return to Liguria, only this time with Genoa.
However, Allegri insists that the Italy international is going nowhere, claiming that the enigmatic attacker is thinking of nothing other than getting himself back in peak physical condition after his exploits at Euro 2012.
"Cassano will stay," the former Cagliari boss is quoted as saying by Gazzetto dello Sport. "He is doing well at the moment and is training well."
Elsewhere, Allegri declined the invite to enter into a slanging match with former Rossoneri midfielder Gennaro Gattuso, who recently claimed that both he and centre-half Alessandro Nesta were pushed out of San Siro by the trainer.
"Talking about things that have past and stirring up controversy is of little use to anyone," the 44-year-old told RTL 102.5.
"I have been fortunate to have had the opportunity to coach this squad for two years. I have won a league title and a Supercoppa and for me, that's been the most important thing."
Allegri took charge of Milan two summers ago and immediately led the club to their first Scudetto since 2005.
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