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The Red Devils are facing a race against the clock to sign the Morocco star before Friday’s 11pm deadline.
United have already had one loan bid of around £2m turned down by Fiorentina, who favour selling Amrabat on a permanent basis.
The likes of Nottingham Forest, Fulham and Galatasaray have complicated matters by bidding for Amrabat.
But the Moroccan only wants to join United, and has held out all summer in the hope of moving to Old Trafford.
And the Athletic say Hargreaves has flown to Florence to negotiate a deadline day deal for the midfielder.
Hargreaves, who used to work for Adidas, moved to United in March but has only started in his new role this summer.
Fiorentina are happy to agree to a loan deal, provided United include an obligation to buy in the deal.
However, how that looks in reality is up for dispute, as United would likely want to include a series of clauses such as the need to make a specified number of appearances.
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