The 20-year-old centre-back has impressed on loan at PSV Eindhoven and is believed to be keen on staying in the Netherlands.
But PSV are yet to try and sign him on a permanent deal and the centre-back will be returning to Everton during pre-season this summer.
Everton decided against taking up the option on Conor Coady’s loan and allowed him to return to Wolves at the end of the season.
And it has been claimed that Branthwaite is currently set to be part of Everton’s plans next season.
The club have been left impressed with his performances at PSV and he is rated highly at Goodison Park.
But the final decision on whether he will be part of the squad next season will rest with Toffees boss Dyche.
The Everton manager will take a look at Branthwaite during pre-season before taking a decision.
But there is now a good chance that the centre-back will be part of the Everton squad next season.