Konate, 27, joined Liverpool from RB Leipzig in 2021 for £35M on a five-year contract that could not be extended this summer as talks over his high wages broke down.
Despite there being reports earlier this year that an extension could be close to being agreed, the France international will leave Liverpool as a free agent when his contract expires this summer.
The defender made 183 appearances for Liverpool in all competitions and won the Premier League, FA Cup, and two League Cups during his time on Merseyside.
As Liverpool seek to sign a replacement, Konate has already decided on his next destination as reports in Spain state that Real Madrid president Florentino Pérez has reached an agreement with the former RB Leipzig star.
This is according to a report from Onda Cero’s Alberto Pereiro that also states that Konate will be snapped up once Pérez wins the upcoming election.
The moves comes one year after Trent Alexander-Arnold left Liverpool for the Spanish capital, as the La Liga giants continue to draw players away.
Liverpool sacked boss Arne Slot on Saturday, with Andoni Iraola the front-runner for the job as huge changes overhwhelm the side ahead of what will be a very busy summer transfer window.