The Reds will have to shell out for his release clause, but they are unlikely to face any further problems.
Jurgen Klopp is eager to improve his options at the back this summer due to injuries suffered by Virgil van Dijk, Joe Gomez, Joel Matip and Fabinho last season.
And Konate has been on his radar for some time, with ESPN reporting the youngster has already had a medical exam at the club.
He would have undergone the necessary checks a few weeks ago and will sign a five-year contract after competing for France in the European Under-21 Championship.
Konate is highly regarded and is considered one of the best young defenders in Europe.
His performances alongside Dayot Upamecano for Leipzig saw him catch the attention of many clubs across Europe, but Liverpool appear to have won the race to sign him.
Liverpool will have to pay their full release clause in one go, meaning they can’t use the approach they took with previous transfers and pay in installments.
The Reds secured Thiago Alcantara and Diogo Jota for a total of £ 9.5million in advance last summer, paying the rest in installments.
The money for Alcantara will be paid to Bayern Munich in installments of £ 5million each year, while Wolves will receive the remainder of their £ 41.5million transfer fee in installments.
But for Konate, they will have to pay his entire £ 35million in one go.
Liverpool had to wait until the last day of the Premier League season before securing Champions League football for next season, and it looks like that played a major role in their attempt to sign Konate.
Missing out on top European competition would have hit Liverpool financially, meaning they might have turned to cheaper targets.
But as they finished in the top four, the decision has now been made to trigger his release clause and close the deal.
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Liverpool have reportedly been following him for several years now, dismissing any suggestion that this is an impulse buy.
The future of Nat Phillips and Rhys Williams is still up in the air after the pair’s unlikely senior run.
Following the calamitous string of injuries the club suffered, Liverpool were forced to play the two untested squad players in key periods of the campaign.
After the season ended on Sunday, Klopp was quick to praise the pair.
He said, “These two boys, playing like that, it’s amazing, absolutely amazing.
“It was a crash course in a Premier League education, and they learned so much,” he said. “It’s a sign for all of our kids in Liverpool at the academy. It is possible – it shows that it is possible… you just have to work hard.