United are badly in need of midfield reinforcements due to long-term injuries to Paul Pogba and Scott McTominay.
Fernandes, 25, has been linked with a move to Old Trafford for many months, but United were previously unwilling to meet Sporting's 80 million euro valuation (£67 million, $88 million).
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A deal has reportedly now been agreed for an initial fee of 55 million euros with another 25 million euros in performance-related add-ons.
Fernandes has scored 63 goals in 137 appearances for Sporting since returning to his homeland after spells with Udinese and Sampdoria in Italy.
He was also part of the Portugal side that won the inaugural Nations League in June and has scored twice in 19 international caps.
There had been mounting pressure on United's executive vice-chairman Ed Woodward to land at least one marquee name in the remainder of the transfer window.
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Woodward, who has overseen the club's poor recruitment over the past seven years, had been the target of the fans' anger in a 2-0 home defeat to Burnley last week that left the Red Devils still six points adrift of the Premier League top four in fifth.
United's chances of a top-four finish will depend greatly on how they fare in their next two league games at home to Wolves on Saturday and then away to fourth-placed Chelsea on February 17.
Even if he is signed in time, Fernandes would not be eligible to face Manchester City in the second leg of United's League Cup semi-final on Wednesday.
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