Kovacic is contracted to the Spanish capital club until 2021, but his lack of playing time has seen him linked to several clubs. With just 30 minutes of playing time in the league under his belt this term, further interest is expected in January.
Sanchez admits Madrid received several offers for the Croatia international in the last transfer window, including from Spurs, but they still see him as having a key role in their future and wish to hold on.
"Kovacic is not for sale, we will never sell him!" he told Sportske Novosti.
"If there are any offers for him in January, we will reject them. Last summer there were a lot of offers and questions about him.
Despite his limited role, Kovacic would rather remain at the Santiago Bernabeu, according to the director.
"Mateo is a smart guy, he knows he would have played in the starting XI in each of those teams that want him but he is aware we count on him too.
"He is one of the players the club's future relies on."