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Ole Gunnar Solskjaer’s side are working hard to add a striker, with Bournemouth’s Josh King a £27m target before the window closes.
But they have also reinforced their youth ranks with the capture of England Under-20 international Bishop.
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“The opportunity to join Manchester United is a dream come true,“ Bishop said. “This club has a great record of developing goalkeepers and I cannot wait to work with the coaches here to improve every single day.
“I want to take the chance to thank everyone at Southend United for everything they have done for me throughout my time there; without their support, this move would not have been possible.”
Bishop made 39 appearances for Southend.