United, who are fifth in the Premier League, are looking to strengthen their midfield for the remainder of the campaign with record signing Paul Pogba recovering from ankle surgery and Scott McTominay nursing a knee injury.
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The BBC reported Sporting valued the 25-year-old Fernandes at 60 million pounds ($77.97 million) while Sky Sports said the deal could see United defender Marcos Rojo move the other way.
Fernandes scored two goals as Sporting beat Vitoria Setubal 3-1 on Saturday and head coach Silas was unsure if the Portugal international would be available to face Benfica on Jan. 17.
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"I can't guarantee any of these things because I don't know. Bruno is a huge player and all players like him have a lot of market," Sky Sports quoted Silas as saying.
"I don't like to think about it, but I'll be thinking of alternatives in case Bruno leaves. I hope it doesn't happen, but we have to start thinking that."
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