The 27-year-old is set to put pen to paper on a five-year deal at the San Siro, ending a frustrating two-year spell at Chelsea.
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Nkunku joined the Premier League giants in the summer of 2023 but a serious injury in his first pre-season meant he fell down the pecking order almost immediately.
Milan will pay Chelsea a fee in the region of €35m plus add-ons and a sell on clause that could take the deal to €42m should certain conditions be met.
He is now set to undergo his medical at Milan with the deal now expected to go through before the September 1st transfer deadline.