The 26-year-old defender has reached a critical point in his contract talks.
Madrid have been making moves in the background, making sure he is encouraged to avoid extending his stay at Anfield. Their message is that he should wait it out so he can walk away for free at the end of the season - then step into the Bernabeu as part of their next era.
It is a strategy they used successfully when Trent Alexander-Arnold made the same move, and there is a growing belief in Madrid that Konate will follow the same path.
Liverpool are not prepared to concede the fight yet.
Talks have remained open throughout the international break, with top figures at the club heavily involved in the discussions. The club’s position is that an agreement can still be found if Konate’s demands are met, but so far, those demands have proven difficult to satisfy.
Konate has already turned down three offers, standing firm on his view of his worth.
Madrid are confident they can meet his expectations, and insiders in Spain believe he is a realistic target. They see a defender entering his prime, available without a transfer fee, and capable of immediately strengthening their back line.
The financial package would be costly, but it is not expected to hit the levels Madrid committed to for Alexander-Arnold.
Despite some reports suggesting a deal is close, sources at Liverpool are adamant that nothing has been agreed. They stress Konate has not made a commitment to Madrid, or any other club.
Sources are also keen to point out that while the door to Liverpool is not closed, the chances of a breakthrough are diminishing as the months pass.
The concern for Liverpool is that this situation feels like history repeating itself.
Allowing Alexander-Arnold’s contract to run down remains a sore point, and there is frustration that another key player could yet be lost in the same way.
