The 21-year-old, who somewhat surprisingly missed out on a spot in the final England squad for Euro 2024, is currently being heavily linked with a move to the 20-time English champions.
Man United are looking to bring in a replacement for Raphael Varane, and it is understood that Branthwaite is viewed as the club's leading target when it comes to central defenders.
However, according to talkSPORT, the Red Devils are 'reluctant' to pay Everton's valuation of the defender, with the Toffees not thought to be willing to let him leave for under £70m.
The report claims that Man United's new minority shareholder Sir Jim Ratcliffe has changed the transfer strategy since taking over the football department at Old Trafford.
Everton are said to value Branthwaite at around £70m
Ratcliffe is said to be unwilling to pay over the odds for players, with the club's recent deals for the likes of Antony and Casemiro being heavily criticised.
Everton could therefore potentially price Branthwaite out of a summer deal, with the Red Devils being forced to switch their focus elsewhere if it becomes apparent that the Toffees will not negotiate.
Branthwaite enjoyed a strong 2023-24 campaign for Everton after returning to Goodison Park last summer following the completion of a successful loan spell at PSV Eindhoven.
The Englishman made 41 appearances last season, including 35 outings in the Premier League, scoring three times, and he was key to Everton's strong finish to the season.
Sean Dyche's side won five of their last eight league fixtures of 2023-24, keeping clean sheets in all of those successes, with Branthwaite not missing a minute during that run.
Which other centre-backs are of interest to Man United?
Nice's Jean-Clair Todibo is also being linked with a switch to Man United, with the 24-year-old having a strong season in France, making 33 appearances for his Ligue 1 side.
There has also been speculation surrounding a potential move for Ronald Araujo, as the Uruguay international is stalling on a new contract at Barcelona.
Antonio Silva, who will represent Portugal at Euro 2024, is also said to be admired, but Benfica are not thought to be willing to let the 20-year-old leave for less than his £85m release clause.
Juventus' Bremer and Bayer Leverkusen's Edmond Tapsoba have also been linked with moves to Old Trafford over the last few months.
Man United remain in talks with Jonny Evans over a new contract at Old Trafford, while Lisandro Martinez is set to stay, but the club are thought to be open to offers for both Harry Maguire and Victor Lindelof.