Garnacho accepts he has no future at United under manager Ruben Amorim and plans to move on this summer.
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The Argentina international has emerged as target for Serie A champions Napoli, where former teammate Scott McTominay has thrived.
However, The Sun says Garnacho wants to stay in the Premier League and has welcomed interest from Chelsea.
A source said: “Alejandro knows the Premier League is the best in the world.
"And while he has had some good moments at United, he wants to establish himself as a world star.
“England is the best place to do that and Chelsea have assembled a lot of good young players.”