Valencia is a free agent this summer having been released by the Red Devils following a decade at the club.
A number of sides from the USA are also understood to be interested in the 33-year-old. As yet, Valencia is yet to make a decision on his career after Man United.
However, it seems strange that the Blades would be interested.
Admittedly, Valencia would bring huge amounts of Premier League experience with 325 appearances in the division. The right-back has also won the title twice, along with the Europa League, FA Cup and two League Cups.
Despite that, there are serious question marks over whether Chris Wilder needs a player like Valencia in his squad.
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Why Sheffield United don’t need Valencia
Wilder plays a well worked 3-4-1-2 formation that has lead to two promotions in his three seasons as manager.
As a converted winger, Valencia would arguably perfectly fit the role of wing-back. Yet unlike fellow Man United veteran Ashley Young, the Ecuador international does not have the versatility to play on both flanks.
Valencia is a right-sided player through and through. Converting him to the left at this stage of his career would be a waste of time.
The Blades do need some support/competition on the left for Enda Stevens. But on the right they are well stocked with George Baldock and Kieron Freeman as options.
The only scenario where they would need to recruit there is if one were to leave.
Baldock has been linked with Celtic, with the Express claiming the Bhoys made an enquiry about a £3m deal. The 26-year-old is about to enter the final year of his current contract, but apparently the Blades are keen to keep him.
Also, how would the South Yorkshire side afford to pay Valencia? It was only in March this year that the Mirror reported the South American earned a whopping £100,000-a-week. The Blades could not afford that.