The centre-back has impressed in Serie A this term, making 23 appearances in all competitions.
The 24-year-old has become a key member of the team, and may be heading to England if media reports are to be believed.
However, Grada3 reports Real are only interested in selling Le Normand if someone gets close to his €75m buyout clause.
United may have to pay the buyout clause to force a sale, or negotiate with Real Sociedad in the hopes of reaching an agreement.
Le Normand has a contract with Sociedad until 2024.