United had a scout posted a week ago to check on Muharemovic in action against Cremonese.
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The 1-0 win marked the Bosnia international's 50th appearance for Sassuolo.
Bosnia's Sportsport says United see Muharemovic as a potential successor for Harry Maguire.
Maguire's contract is running down this season and there remains doubts about whether he will sign a new deal.
Muharemovic, 22, has a contract with Sassuolo to 2031.