The 21-year-old French defender is a priority target for Liverpool and there are claims that the club are close to working out a deal with the player.
He has a €41.5m release clause in his contract with RB Leipzig, which makes it a relatively straightforward deal to do if a club are prepared to pay that figure and he wants the move.
It has been suggested that Konate is close to agreeing to a move to Liverpool and has even undergone part of his medical with the Reds.
But according to French sports daily L’Equipe, his entourage have denied the medical claims and stressed that he underwent a few routine tests given his recent injuries.
The defender’s camp have not denied the talks with Liverpool and the Reds are very much in the race to sign him.
But claims of an imminent deal have been played down and more clubs are still in the running for his signature.
There are suggestions that RB Leipzig have even offered him a new contract to stay at the Bundesliga club.