The Italy international played 29 games last season, but was rotating with David Ospina later in the campaign.
Manager Gennaro Gattuso is not sure who will be his no.1 going forward.
The 23-year-old is supposedly wanted by the Red Devils, who may move David De Gea on after a series of poor performances in the past two seasons.
The player's agent Federico Pastorello admits a transfer or loan is a possibility.
"Alex needs to accumulate as many starts as possible to grow more and more," Pastorello told Rai Sport.
"At his age there are goalkeepers who have been immovable for a long time.
"If we do not succeed, we can consider going out on loan.