The Italian defender has been routinely linked with a departure from Old Trafford after failing to hold down a regular first-team place at OId Trafford under Jose Mourinho.
According to The Mirror, United have put off both AC Milan and Napoli with their £15m valuation of the Italy international who is deemed surplus to requirements at United.
The impasse in negotiations has piqued Benficas interest, as they attempt to assemble a side that can challenge Portos domestic dominance in Portuguese football.
According to the report, Benfica were knocked back when they enquired about taking the 28-year-old on loan in the January window.
They re-opened talks with United after their first-choice right-back Tyronne Ebuehi suffers a serious injury in pre-season.
The report claims Darmian would prefer a move back to Serie A, but is willing to listen to what Benfica have to offer if they agree to meet his £70,000-a-week wages.
The Italian has two years left on his Old Trafford contract after arriving at the club from Torino for £13 million in 2013.
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