Football Insider says they would rather sell other stars, and will do everything they can to keep Branthwaite next season.
Everton are said to have started discussions with the defender, to persuade him to stay at the club.
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Manchester United are eager to sign the youngster.
Branthwaite's contract with Everton runs until the summer of 2027.
Instead of Branthwaite, they would be willing to sacrifice midfielder Amadou Onana, 22.