The 21-year-old has been a key player for the Toffees this term, featuring 31 times under Sean Dyche.
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His form resulted in a maiden England call-up for the recent friendlies against Brazil and Belgium.
Branthwaite did not make his Three Lions debut after being left on the bench.
But the centre-back is widely seen as the future of England’s defence.
And the Telegraph claims United are now lining up a bid amid doubts over the futures of Raphael Varane and Harry Maguire.
Both players are out of contract in 2025, with Varane a target for clubs in Saudi Arabia.
As for Maguire, there is an option to extend his deal until 2026.
But West Ham are ready to lure him to London with the offer of first-team football.
And with new United owner Sir Jim Ratcliffe ready to trim the fat, both players could be sold to make room for fresh faces.
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Branthwaite would certainly fit the bill, having already impressed on loan at Dutch giants PSV Eindhoven.
It’s believed he is valued by Everton at over £50million.
The Toffees are hoping to beat relegation despite being docked six points for breaching financial rules.
But their chances of keeping Branthwaite will be virtually zero if they drop down to the Championship.
United are also in the market for a striker to play back-up to Rasmus Hojlund, while they are also keen on a right-back.
A new central midfielder could also be on the agenda should Casemiro also depart.
But it’s Branthwaite who is currently top of the list, with the youngster still dreaming of making England’s Euro squad.
Boss Gareth Southgate said: “He’s played consistently well.
“We watched him as a back-up centre-back at the Under-21 finals last year and if you would have said then he would play as consistently well at PL level as he has, I would have questioned that.
“That is a credit to him. He’s good with the ball, shows good composure and mentality and we don’t have many left-footers.”
Jarrad Branthwaite’s career stats
Those numbers in full…
- Carlisle United, 2019-2020: 14 games 1 goal
- Blackburn Rovers, 2020-2021: 10 games 0 goals
- PSV Eindhoven, 2022-2023: 36 games 4 goals
- Everton, 2019-2024: 44 games, 3 goals
- England U21s, 2023-2024: 6 games, 0 goals
- Trophies: Dutch Cup (PSV); U21s Euros (England U21s)