A number of second-tier sides are keen and have opened talks over a possible fee, with the interest coming after the academy graduate spent last season split between two Championship loan spells, reports the Athletic.
He began the campaign at Sheffield Wednesday, winning back-to-back player of the month awards across a 21-appearance run at Hillsborough, before United sent him to Norwich City in January rather than extend the Owls deal. His time at Carrow Road lasted just one substitute appearance, however, after he picked up a hamstring injury in training days after his debut; United opted to bring him back to Carrington for his rehabilitation rather than leave him with Norwich, a decision that left Canaries boss Philippe Clement publicly frustrated.
Regarded by many at Carrington as Luke Shaw's long-term successor, Amass is an England Under-19 international who made his senior Manchester United debut on his 18th birthday and has gone on to make seven first-team appearances, several of them under previous manager Ruben Amorim during a defensive injury crisis.
He had originally been pencilled in for a full season on loan after United's summer signing of Paraguay Under-20 international Diego Leon pushed him down the pecking order, and he has since impressed during pre-season under permanent boss Michael Carrick, featuring in friendlies against Wrexham and Rosenborg and scoring in the 5-0 win over the Norwegian side.
Carrick, who took permanent charge in May after guiding United to a third-place Premier League finish and Champions League qualification during his interim spell, has yet to indicate whether he sees a first-team role for the left-back this season.
Newcastle United's Lewis Hall has previously been mentioned as an alternative left-back target for United this summer, though the Magpies are said to be reluctant to sanction a sale, leaving Amass's Championship suitors to press on with their interest in the meantime.
Should a permanent deal be struck at United's £6m valuation, it would represent a significant fee for a player yet to make a Premier League start.