The Red Devils are currently keeping a close eye on the defensive market, as Eric Bailly is preparing to follow Axel Tuanzebe and Phil Jones in leaving the club, while Harry Maguire also continues to be linked with an exit.
Maguire's departure would put Man United in the market for another centre-back, and Jonny Evans is seemingly a option, with the Northern Ireland international representing the club during pre-season.
However, a recent report claimed that Branthwaite was also a target, with the 20-time English champions looking to bring in a low-cost signing at the back.
There had been suggestions that the 21-year-old, who spent the 2022-23 campaign on loan at PSV Eindhoven, could be available for as little as £6m.
However, according to Football Insider, Everton have informed Man United that it would cost them £25m to sign him during this summer's transfer window.
The Toffees are in a strong position when it comes to the defender's future, as he has another two years left to run on his contract at Goodison Park.
Branthwaite started his professional career at Carlisle United, making 14 appearances for the club before joining Everton in January 2020.
The defender has only made 13 appearances for the Toffees in all competitions, though, and he represented Blackburn Rovers on loan during the 2020-21 campaign.
Branthwaite has featured on 10 occasions in the Premier League, six of which came in 2021-22, but the most successful season of his career came last term.
The centre-back featured 36 times for PSV during the 2022-23 campaign, scoring four times, with 27 of those appearances coming in the top flight of Dutch football.
Branthwaite helped PSV win the KNVB Cup last term, while the Red and Whites finished second in the Eredivisie table to qualify for the Champions League third qualifying round.
Man United have already made two signings this summer, bringing in Mason Mount and Andre Onana, while Rasmus Hojlund's arrival from Atalanta BC is set to be confirmed on Saturday afternoon.