During the early weeks of the recent summer transfer window, Man United were in deep discussion over a move for the young England international, and subsequently made two bids after it was reported they had agreed personal terms with the player's representatives.
However, both were rejected and came nowhere near matching the £75m valuation Everton placed on the player.
Branthwaite was part of an Everton defence that ranked fourth in terms of goals conceded last season, only bettered by Manchester City, Arsenal and Liverpool, and won his first England cap in June.
After undergoing surgery in the summer though, it has been a frustrating start to the season for the defender, as he missed the first eight games of the campaign, and picked up a recurrence almost immediately after his return.
Since making a full recovery though, Branthwaite has now found himself out of the team, being kept on the bench in favour of Michael Keane, whose recent form was rewarded by Dyche.
Dyche leaves door open for Branthwaite exit
Speaking in his pre-match press conference ahead of Everton's trip to West Ham United on Saturday, Dyche revealed that every player has their price, and if it is met they will be sold.
Everton are in the process of being taken over by the Friedkin Group, after eight years under the control of Farhad Moshiri, and while Dyche is unaware of how the new owners plan on running the club, his words on Thursday will have been of interest to Man United supporters.
"I don't know any of their [the new owners] plans, their thoughts or feelings about the club at this time or the finances. So that would clearly be a new decision.
"The current decision would be that it is likely that if somebody bid enough money for any player - forget about Jarrad, it is not relevant [just to mention] Jarrad - any player at this football club as you have seen over the last couple of windows. If someone offers enough money then they go." Dyche claimed.
"Alex Iwobi was like that a day or so before the deadline [in 2023], I didn't want to lose Alex but they said 'Look, this is a deal we've got to do.
"I said 'ok' and that's the way it goes so therefore I better mould it towards the next lot of players and how many I can get in and use. If the number's right the player gets sold if the number isn't right they don't."
The number evidently was not right over the summer though, as Everton rebuffed two advances from Man United for the defender, despite their well-documented financial struggles.
Will Branthwaite look to move on?
Very little has come out of Branthwaite's camp since the huge transfer interest in him from the Red Devils began.
Everton fans will be glad that the young defender has not gone on record publicly stating his desire to leave, as the likes of Anthony Gordon and Amadou Onana did before departing recently.
After selling Onana, Ben Godfrey and Lewis Dobbin early in the summer window, Everton ensured they passed all PSR regulations, allowing them to up the asking price for Branthwaite to £75m, knowing that they were in no immediate rush to sell.
However, with few valuable assets left at the club given the sorry state of their finances in Moshiri's final years as owner, there may come a point where cashing in on the 22-year-old becomes a necessity, regardless of whether the Friedkin Group provide a cash injection.
The last thing the club wants, especially once they move into their new stadium at Bramley-Moore Dock, is more PSR troubles, and at present, Branthwaite is the only obvious player in the squad who could be sold on for profit, and after finding himself out of the team recently, the club may not be able to ask for as much as they did this summer.