Man United is supposed to weigh whether they have to sign a replacement for Onana, 29, after a series of high -profile errors between the sticks.
Various reports have Milinkovic-Savic, 28, coupled with a move to Old Trafford after his impressive season at Torino, but it seems that United will miss Napoli.
According to Transfer Guru Fabrizio Romano, the Serbia International is close to the side of Antonio Conte, while Cyril Ngonge will probably go on loan.
Leeds United was also interested in Milinkovic-Savic while the Premier League newcomers were struggling with their own keepers.