The Guinea international, 22, has established himself as one of the Bundesliga’s most-coveted midfielders since joining RB Leipzig last summer.
And Klopp has made him his top transfer target following the club-record capture of Mohamed Salah from Serie A giants Roma.
Leipzig have repeatedly stated they will not sell Keita to Liverpool this year, with a trio of bids already rejected by club chiefs.
And Klopp provided a humorous update on the situation in the wake of the Reds’ 3-0 pre-season win over Hertha Berlin yesterday.
Speaking to Sky Deutschland, he joked: "Our next offer for Keita is €300m [£268m]!"
In case anyone was fooled by Klopp’s comment, he stressed it was a joke.
And he added that he would not be discussing Liverpool’s transfer business.
Keita is not the only player to have been linked with a move to Anfield of late.
Klopp is still thought to have his eye on Southampton centre-back Virgil Van Dijk.
Arsenal’s Alex Oxlade-Chamberlain has been talked up as being on Liverpool’s radar too.
However, Starsport understands a move for the 23-year-old is not close.