The Red Devils want to bring in younger, low cost players to improve their squad.
Per Mundo Deportivo, Faye may be one of those candidates, should he want to make the move.
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Faye is an impressive defender who could play for United at centre back next season.
The Old Trafford club are looking to move along Raphael Varane and Jonny Evans in the off-season.
For their part, Barca would prefer to hold onto Faye, as he is only 19 and can play at left-back as well.