Despite the approach, the Cherries have made clear that the England international is not for sale under any circumstances.
Scott, who was born in Guernsey, began his career at Southampton before joining Bristol City in January 2020, where he quickly established himself as one of the Championship's most promising young midfielders.
He won the EFL Championship Young Player of the Season award in 2022-23, catching the eye of Manchester City manager Pep Guardiola, who described him as an "unbelievable player" after a cup tie between the two clubs.
Bournemouth completed his signing that August for a fee reported to be around £25million, and Scott has since gone on to establish himself as a regular in Andoni Iraola's side, overcoming a series of injury setbacks along the way.
Bournemouth are understood to have already offered Scott a new contract earlier this year — the second offer made to the midfielder.
Even if he does not sign a new deal, Bournemouth are still steadfast in their stance that he will not be sold this summer.
His current contract at the Vitality Stadium runs until 2028, giving the club no pressure to sanction a sale.
Scott has continued to develop into a full England international, and Bournemouth are keen to build their squad around him rather than cash in this window.
Manchester United's approach reflects their continued search for midfield reinforcements this summer, though they face a firm rejection from Bournemouth over any potential deal for the 22-year-old.