Sky Italia says an agreement between the two clubs is now close.
Milan will pay €33m to sign Botman after his agents met Milan in February, reaching an agreement over a €2.5m-a-year deal.
Botman has recently confirmed that both Milan and Newcastle tried to secure his services during the winter transfer window.
Milan are expected to see Alessio Romagnoli leave the club at the end of his contract in June. The Italy international is in advanced talks with Lazio and has also been linked with a move to Juventus.
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