Sky Sport Italia claims the Brazilian landed at Malpensa airport just after 12:20 CET and was whisked away to the Gallarate hospital, where he will have a medical in the presence of Armando Gozzini - a medic working on Milan's behalf.
And, should he pass his tests, the Serie A club will then finalise a deal with Manchester City, who have asked for £12.3 million (€15m) for a permanent transfer. But Milan chief Adriano Galliani is expected be in line to want the price reduced.
In the meantime, the diminutive hitman has expressed a desire to win the Scudetto with his prospective club, should the move go through as planned.
"I am happy. I want to play with Milan because they are an excellent squad," Robinho said, according to Sky Sport 24.
"I want to win the Scudetto."
Robinho's impending signing may well also spell the end of Marco Borriello's time at Milan as vice-president Adriano Galliani confirmed to Sky Sports that, "For every player who is sold, comes one new player".