The 19-year-old defender has already made 48 appearances for Monaco in all competitions and particularly caught the eye prior to the curtailment of the 2019-2020 French domestic season.
Recent reports suggested Man Utd had made an opening bid of £22.28million (€25m) for the France youth international, which Monaco were quick to knock back.
Kovac has declared Badiashile, who has played a full part in Monaco's opening two Ligue 1 matches of the new season, is going nowhere for at least another year.
"Our aim is to take him to the next level," he said. "If he plays a lot of matches with us in Ligue 1, which is a very good league, he will improve, that is certain.
"We do not want to sell him that is very clear. He will stay here this season. I think that this is the best solution for him. He has his club here, his family. He knows the environment."
Badiashile made his debut for Monaco in November 2018 and signed a new deal last December that runs until 2024.