The Italy international has been heavily linked with a move away from Stadio Olimpico, but Roma coach Rudi Garcia ruled it out earlier this month.
However, Milan - yet to announce any details of the transfer - confirmed on Thursday that Destro is set to switch to San Siro.
Destro has made 16 league appearances for Roma this season, although half of those have come from the bench.
The 23-year-old has scored five goals in that time and Milan will be hoping the forward can help lift them into contention for European qualification.
Milan sit 11th in Serie A, 23 points adrift of league leaders Juventus.
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