Muharemovic left Juventus for Sassuolo in the summer of 2024, initially on loan.
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The promising centre-back has scored two goals and two assists in 14 Serie A matches this season.
Il Gazzetta di Modena says United have been scouting Muharemovic.
The English giants scouted Muharemovic when Sassuolo played against Bologna on Sunday and representatives are said to have been impressed.
Aston Villa and AFC Bournemouth are also showing interest in the defender.
Muharemovic has a contract with Sassuolo that runs until the summer of 2031.