The France under-21 international is one of the Bundesliga’s hottest defensive commodities after impressing for Leipzig.
However, according to Sky Sport in Germany, United and other suitors have cooled their interest in Konate.
They add that RB Leipzig plan a meeting as soon as possible to renew Konate’s contract.
Konate is under contract at the Red Bull Arena until 2023, but the Bundesliga high-flyers want to give him a new deal.
The 6’4″ tall central defender joined Leipzig from Sochaux on a free transfer in 2017.
Prior to a torn muscle fibre injury which sidelined him from October until the Bundesliga restart, he was a regular for Julian Nagelsmann’s side.