United know that defensive issues from this season cannot be repeated next term.
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Raphael Varane and Jonny Evans could well leave in the summer, while Victor Lindelof is also a backup.
Branthwaite, 21, has impressed with the Toffees this season and is now in England reckoning.
Tapsoba, who is 25, has been a key figure in defense for Xabi Alonso's Bundesliga winners.