RB Leipzig rejected a first offer from the Reds last week of £57m.
But Jurgen Klopp is not ready to give up on signing the talented midfielder this summer.
Liverpool are prepared to smash their transfer record to bring Keita to Anfield.
And according to the Liverpool Echo, the Reds will test Leipzig’s resolve once again.
The Bundesliga club have been adamant they do not need to sell as they are financially sound following last season’s success.
Keita helped Leipzig qualify for the Champions League, but the 22-year-old is now desperate to join Liverpool.
It is said the Guinea international has urged Leipzig to grant him his dream move to Merseyside.
The Liverpool Echo add the Reds hope a fee of around £65m will convince the German outfit to let Keita leave.
Klopp has already managed to add Mohamed Salah to his squad in the window after a drawn out saga with Roma.
But having landed the winger last month, Keita is the man wanted to strengthen Liverpool’s midfield.
Lucas Leiva could be joining Lazio in a £5m deal, which would leave the Reds further stretched in that area.
After Liverpool’s 1-1 draw against Wigan in their pre-season friendly last night, Jurgen Klopp refused to discuss potential incomings.
“If whatever I say here would change anything in a positive way I would,” Klopp said. “But I have no influence.
“It is not important what I say, it’s only important what we do. We try to do the job. We feel in a good way. I can’t say anything on players.”
