The French defender is in the final months of his current deal and there had been rumours suggesting he was going to join Real Madrid on a free transfer.
However, interest in Konate cooled after a poor start to this season and he is set to extend his five-year stay at Anfield.
“For a long time we have spoken with the club and we are close to an agreement,” said the 26-year-old after Liverpool’s 2-1 Merseyside derby win over Everton.
“I think everyone wished for that for as long as possible but we are in a good way. For sure there is a big chance I’m here next season. This is what I always wanted.”
Konate missed three games earlier this year after the death of his father, but cut short his compassionate leave to help Liverpool through an injury crisis.
Crowned champions of the Premier League less than a year ago, Arne Slot’s side have suffered a difficult campaign on and off the field.
The death of forward Diogo Jota cast a shadow over the club before the season began.
Defeats to Manchester City in the FA Cup and Paris Saint-Germain in the Champions League has ended any hope of silverware for the Reds.
But Konate is focused on ending the season on a high by securing Champions League football.
Liverpool opened up a seven-point lead over sixth-placed Chelsea thanks to Virgil van Dijk’s late winner to beat Everton.
“It was a tough year and I think if everyone knew exactly what happened to me, they could understand many things, which kind of sacrifices I’ve done for this club,” Konate added.
“Right now we focus on the end of the season and make sure we are qualified for the Champions League and after we can take the time to talk about the season because it’s going to be a big part of my story and it’s sad in one part.”
Extending Konate’s stay will avoid the immediate need for Liverpool to go in search of a centre-back signing.
Jeremy Jacquet will arrive in the summer after a £60 million ($81 million) deal was done with Rennes for the 20-year-old in January and Giovanni Leoni, 19, will return next season from a serious knee injury sustained on his debut in September.
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