BBC Sport says Barca and United have agreed terms "in principle" over a loan deal for Rashford.
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The England attacker has already approved the move, making Barca his priority destination after being transfer-listed by United at the end of last season.
Talks have been ongoing between intermediaries and a verbal agreement has now been reached.
The terms will be for a season-long loan with an option to buy.
Barca have turned to Rashford after being snubbed by Athletic Bilbao winger Nico Williams and struggling to find agreement with Liverpool for Luis Diaz.