The Red Devils were keen to sign the 22-year-old in the summer but failed with two offers, including their second bid worth around £45m plus add-ons.
Branthwaite's stock has risen considerably since breaking into Everton's first team last season and establishing himself as an important player under manager Sean Dyche.
The 6ft 5in centre-back made 41 appearances for the Toffees in all competitions in 2023-24, including 35 Premier League outings, helping the club avoid relegation and climb up to 15th place.
Branthwaite, whose impressive performances were also recognised by England earlier this year, is yet to represent Everton in the new campaign due to injury, with Dyche's men losing each of their first three top-flight fixtures and conceding 10 goals in the process.
Branthwaite remains on Man United's radar
Everton are determined to keep hold of Branthwaite long term, with the defender under contract at Goodison Park until the summer of 2027.
However, the Liverpool Echo claims that the Toffees are bracing themselves for 'continued interest' in Branthwaite from long-term admirers Man United.
Despite spending big on Leny Yoro and Matthijs de Ligt from Lille and Bayern Munich respectively this summer, Man United are said to be exploring ways in which they can reinforce their centre-back options further next summer.
It is claimed that the Red Devils will continue to monitor Branthwaite throughout this season as he remains a player of interest, but Everton will not let their star defender leave on the cheap.
Indeed, it is understood that Everton value Branthwaite - who has also been linked with rivals Liverpool - at around £80m, the same fee Man United forked out to sign Harry Maguire from Leicester City in 2019.
Who else could Man United look to sign in 2025?
Man United spend in the region of £180m on five new signings in the summer, with Yoro and De Ligt followed to Old Trafford by striker Joshua Zirkzee, full-back Noussair Mazraoui and defensive midfielder Manuel Ugarte.
However, a recent report claims that Sir Jim Ratcliffe and co are targeting four new high-profile players as part of an ambitious transfer plan for next summer.
Man United are said to have identified Crystal Palace attacker Eberechi Eze as a potential target and have joined the likes of Manchester City and Tottenham Hotspur in the race for his signature.
The Red Devils are also believed to be keen to strengthen in midfield and at left-back, with Fulham's Antonee Robinson, Bournemouth's Milos Kerkez and Brest's Bradley Locko among their defensive targets.