According to The Athletic, the French Under-21 international seems set for a move to Anfield as Liverpool look to activate his €40 million release clause.
Konate has spent the last four years in the Bundesliga and is one of the most highly rated young centre-backs in Europe.
He made his debut for Sochaux at 17, making just 12 appearances for the French club before moving to Leipzig in June 2017.
Konate played 63 games across his first two seasons in Germany but injuries have held him back recently, limiting him to just 15 appearances in the current campaign.
Still, the towering defender gained valuable Champions League experience as Leipzig finished second in their group, ahead of Manchester United.
He remained on the bench throughout both legs of their round of 16 tie against Liverpool as they exited the competition courtesy of a 4-0 defeat on aggregate.
Leipzig have already announced the departure of Dayot Upamecano, after Bayern Munich met his release clause last month.
Now Konate looks to be following suit, with Jurgen Klopp determined not to be caught out again at the back.
The decision to sell Dejan Lovren without a replacement last summer left him short of options once injuries struck.
Virgil van Dijk, Joe Gomez and Joel Matip have all missed large chunks of the season, forcing Klopp to field a whole host of different partnerships at centre-back.
Midfielders Fabinho and Jordan Henderson have often been asked to fill in, while the inexperienced duo of Nat Phillips and Rhys Williams have been much busier than expected.
Ozan Kabak and Ben Davies both arrived late on in the transfer window but neither is certain of a future at Liverpool beyond the end of the season.
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