A source said: "A deal is almost done. Pedro wants it, United want it and Barcelona accept they have to let the lad go."
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Pedro could be Louis van Gaal's sixth signing of the summer
Pedro is set to become Van Gaal's sixth signing ahead of the new season and take his spending to around £100m.
Memphis Depay (£25m), Matteo Darmian (£12.7m), Bastian Schweinsteiger (£15m), Morgan Schneiderlin (£25m) and Sergio Romero (Free) have already joined.
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According to the Liverpool Echo, Kop boss Brendan Rodgers is willing to let the 18-year-old leave the club on a temporary basis to play first-team football.
Swindon Town have been linked with a move for Kent, having already brought in three Reds on loan this summer.
John Stones - Spotlight on
Chelsea are working on a double deal for Everton centre-back John Stones and Augsburg left-back Baba Rahman.