The 26-year-old Algeria international would add to to the pressure on Memphis Depay who has struggled in his first season at United.
Jesse Lingard has been preferred in recent weeks but the interest in Feghouli would suggest Louis van Gaal wants more options.
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Feghouli joined Valencia in 2010 from Grenoble and has become a key player.
But the club's struggles under Gary Neville, and previously Nuno, seem to have convinced Feghouli to leave.
Valencia are 12th in La Liga, seven points above the drop zone and eight from sixth place, making European qualification for next season look out of reach.
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