The 30-year-old centre-back has been linked with an exit from the Napoli side in Serie A this summer, with his contract due to expire in 2023.
United reportedly failed in their bid to lure the Senegal international away from Italy last summer before the club brought in Raphael Varane.
And according to Calciomercato, the Red Devils were looking to rekindle their interest in the centre-back due to his contract situation.
But the player insisted he wasn’t going anywhere as he pledged his loyalty to Luciano Spalletti’s side.
The former Genk star was greeted by supporters in Napoli after helping Senegal win their maiden Africa Cup of Nations title.
And Koulibaly had a message for the fans who welcomed him to Italy.
Quoted by Tutto Napoli, he said: “This welcome makes me very happy.
“But take it easy because I’m not leaving, I’m not leaving.
“I’m back in Napoli and I’m calm. I thank everyone, I saw all the videos and the things you did when I wasn’t there.
“I am proud to be with you. Thank you all.”
Koulibaly, who has played 19 games in all competitions for Napoli this season, is expected to return straight to the starting XI for Saturday’s clash against Inter.
Napoli come into the game at the Stadio San Paolo one point behind the league leaders.