The England international is thought to have been identified as one of the Red Devils' leading rearguard targets for the summer window but has so far been priced out of a summer transfer.
It is believed that Everton value Branthwaite in the same bracket as Harry Maguire and Josko Gvardiol and are therefore looking for £80m to sell, although a deal could be done for closer to £70m.
However, Man United are currently nowhere near meeting Everton's valuation and reportedly tested the waters with a bid of just £35m, which could have risen to £43m with add-ons.
The Toffees immediately laughed off the Red Devils' opening approach, and as Man United are said to be working with a starting budget of just £50m, a deal is seemingly dead in the water for the time being.
Branthwaite 'frustrated' as Matthijs de Ligt movement made
According to The Mirror, the lack of progress has left the 22-year-old incredibly frustrated, indicating that he wants a switch to Old Trafford to go through ahead of the 2024-25 campaign.
However, Everton are under no immediate pressure to sell their prized asset on the cheap, as he only signed a new contract back in October and is tied to Sean Dyche's side until the summer of 2027.
There were fears that the Toffees may have had to facilitate a summer exodus had they suffered relegation to the Championship, and funds do still need to be raised as a matter of priority.
Everton have already generated over £20m through the sales of Ben Godfrey to Atalanta BC and Lewis Dobbin to Aston Villa, though, and both Dominic Calvert-Lewin and Amadou Onana could soon depart for sizeable fees as well.
With Everton currently showing no signs of softening their stance on Branthwaite, the Red Devils are believed to have switched their focus to Bayern Munich's Matthijs de Ligt, one of Erik ten Hag's former Ajax proteges.
De Ligt burst onto the Amsterdam scene under the Man United boss, reaching the semi-finals of the 2018-19 Champions League before earning marquee moves to Juventus and most recently Bayern.
However, the Dutchman has failed to settle at the Allianz Arena and has apparently informed his agent of his desire to complete a move to Man United, who could capture him for around £40m.
Is a deal for Branthwaite still realistic?
While De Ligt would represent a cheaper and slightly more experienced option than Branthwaite, the Red Devils are still said to have their eye on the latter, who scored three goals in 35 Premier League matches last season.
Branthwaite will soon possess a close connection and huge admirer at Man United too, as Ruud van Nistelrooy - whom he worked under at PSV Eindhoven - is set to return to the club as one of Ten Hag's assistants.
However, unless Everton drastically reduce their asking price or express a willingness to do a swap or part-exchange deal, Branthwaite will be going nowhere this summer.