By SABC Sport
3rd October 2024
The 22-year-old was the subject of two bids from Manchester United, the highest around ã50million which was well below the Toffees' valuation, and a report this week suggested Liverpool were also considering a move.
That prospect remains unlikely as their Merseyside neighbours are unlikely to meet the minimum ã70million fee Everton want for a player contracted until 2027, with the club holding an option for a further 12-month extension.
But it has just added to the narrative surrounding Branthwaite, whose first appearance of the season coincided with Everton's first win last weekend over Crystal Palace.
"There is a lot going on for him outside of what we do, nothing to do with him [but] there are stories everywhere about him," said Dyche.
"But he seems pretty level and pretty much enjoying getting back to playing, that's for sure.
"He seems fine other than being injured, which has been a blow to him.
"It's not a surprise good players are linked with other clubs. I said in the summer he'll be staying here and he is so that's good."
Everton's ongoing financial situation, which has forced them to sell at least one high-profile player a year due to profitability and sustainability rules, means Dyche cannot guarantee that position will remain steady even with the prospect of an imminent takeover from the Friedkin Group.
"The club has a situation which it will still be looking upon," added Dyche.
"If new ownership goes through, that might change things financially in terms of the viewpoint of where it is at and where it wants to go but we don't know that yet. We'll just have to wait and see."
Branthwaite's return to the side and their first win may not be coincidental but Dyche said it would be wrong to place all the responsibility on the centre-back for improving their fortunes after renewing his successful partnership with James Tarkowski.
"Whether it is or it isn't, people will make that story, it's just the way it goes," he said.
"He is rounded enough to know that but there are 10 other players out there at any given time working hard and I thought they worked hard around him on Saturday as he is still getting back to true fitness.
"I know him well enough to know he is well aware of his team-mates and what the importance of the group is."
Everton have honoured former player and manager Joe Royle by naming the driveway at the club's Finch Farm training complex after him.