This latest report says United are still only willing to pay around £40 million for a player Everton value at closer to £80 million at least.
It seems these stories are simply not going to go away and we will have to brace ourselves for constant links with Erik Ten Hag's side, and possibly many others too.
And even if the Dutch manager leaves Old Trafford - which still mgiht happen - it appears likely that United will continue to pursue Branthwaite.
Ideally, as I have said repeatedly, I want the 21-year-old England international to stay at Goodison Park for at least one more season, as I think all Everton supporters would.
However, the persistance of these reports seem to indicate that the pressure will continue to mount from United for a deal to be done.
Meanwhile, the Blues face the nightmare combination of huge debts and continuing uncertainty over the club's future ownership which has just got more challenging over the weekend after 777 Partners proposed takeover finally fell through.
All that means Everton are in a weak position - at least in theory - to fend off rival Premier League clubs who want to take advantage of their situation and take players off them on the cheap.
Although, having said all that, the immediate position is apparently not as drastic with money incoming from the Premier League and TV broadcasters and so there is no need for the proverbial 'fire sale' of players.
Amadou Onana has made clear he wants to leave this summer after the Euros and wishes to use the tournament to advertise himself to potential suitors.
Despite his talent and fleeting moments of genuine dominance in the Toffees midfield, I don't think many supporters will be too devastated if he departs.
He could well be replaced by Kalvin Phillips coming in on loan from Manchester City, although I am personally not convinced that is the right move for the Blues.
Of the Toffees main assets then, that just leaves Branthwaite who would command the biggest fee of the remaining players - along with Jordan Pickford.