The Sun says United are plotting a world record £90m summer move for Koulibaly.
Koulibaly admits he has been flattered by interest in him, saying: "I am pleased that many teams follow me.
"But I want to demonstrate on the field I am at the level of the greatest and I want to show it in the future."
United are ready to trump the £75m Liverpool paid Southampton for Virgil van Dijk - the current record for a defender - to sign their No 1 target, even though Koulibaly admits he might not be worth such a hefty fee.
"I don't know if I'm one of the strongest defenders in the world," he said. "But I always try to give my best."