The Rossoneri are believed to have wrapped up a deal for the Brazil Under-20 international, thus ending their pursuit of a third-choice goalkeeper following Flavio Roma's departure
The Rossoneri have been scouring the market for a back-up for Christian Abbiati and Marco Amelia as Flavio Roma is set to leave the club when his contract expires this summer.
The Brazilian is expected to be in Italy on Monday to finalise his transfer to Milan, who will pay a fee in the region of €500,000 for the shot-stopper.
Gabriel, 19, holds a EU passport and was reportedly also being tracked by Juventus, but has struggled to displace current Cruzeiro No.1 and captain Fabio between the sticks.
However, he is a full Brazil Under-20 international with 15 caps under his belt, which saw him keep goal during the Seleccao's U20 World Cup triumph last year, and will now continue his development in Italy.