Amrabat, who has not appeared for Fiorentina this season amid uncertainty about his future, played for United manager Erik ten Hag at Utrecht.
United have been interested in the 27-year-old for weeks but have been struggling to raise the funds to buy him because of Financial Fair Play considerations and are looking at a loan instead.
Amrabat, one of the outstanding players in last year’s World Cup, would give United a defensive midfield option to play alongside Casemiro.
They are without two injured midfielders in Mason Mount and youngster Kobbie Mainoo, while they have sold Fred to Fenerbahce.
United are also working on bringing in a left-back before the transfer window closes after Luke Shaw joined Tyrell Malacia on the treatment table, with Chelsea’s Marc Cucurella their preferred candidate. They have also considered Tottenham’s Sergio Reguilon and Lyon’s Nicolas Tagliafico.
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