The 21-year-old has been in impressive form for his Merseyside club this season, making 30 appearances in all competitions, and Manchester United are said to be determined to sign him this summer.
Tottenham Hotspur, Arsenal and Real Madrid are also believed to be among the clubs keen on the England Under-21s international, who spent the 2022-23 campaign on loan at PSV Eindhoven.
There have been claims that Everton could be forced to sell Branthwaite this summer due to their financial problems.
However, the centre-back has a contract at Goodison Park until June 2027, and Dyche has said that his club are not prepared to entertain a summer departure for the centre-back.
«We don't want to sell any good players. It's as simple as that and he's proven to be a very good player. We're not in the business of trying to sell players,» Dyche told reporters.
«You only sell players if you have to sell players or there's a problem. There's no problem, therefore I'm just hoping we don't need to sell players. At the minute, we certainly don't so we will see.
»What I saw of him, I liked. When the timing was right, I thought 'go on then, go and enjoy it, go and have a go'. I didn't have to say anything to him, just go and play.
«He's adapted well. There are things he still needs to work on, but you unravel a player slowly, you can't just fast-track everything into them and say 'that's it'.
»So while he's developing nicely and while he's learning, sometimes the hardest thing is not to coach at all when you just step away and go 'no, no, you're fine, you keep doing
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