Both Premier League giants are serious about securing the young English defender this summer.
However, The Standard states that Everton are not in the mood to sell their prized asset.
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The Goodison Park club will look to secure the 21-year-old on a new contract with a higher salary.
That said, Branthwaite is thought to be eager to make a move to a bigger team.
The club may have to accept his sale, although they would only do so for a fee of around 80 million.