Goal understands Liverpool will need to smash the Bundesliga transfer record (€75m/£66m) in an attempt to prise Keita away from RB Leipzig, but their public rhetoric has remained unyielding.
The Reds were expecting to need to fork out €80 million on the Guinean but RB Leipzig, who will enjoy Champions League football in 2017-18, have renewed their refusal to negotiate over the sales of their best players.
"We will definitely not be letting any key players go," RB Leipzig transfer chief Ralf Rangnick stated on Thursday at the unveiling of new signing Jean-Kevin Augustin. "There's nothing that will make us budge.
"It's totally normal for clubs to be interested in our players, but that doesn't affect our stance on the matter."
RB Leipzig, who were promoted to the Bundesliga in 2016, are now one of Germany's wealthier clubs having received a huge amount of investment since being bought by Red Bull in 2009.
Liverpool are hoping to add a central midfielder, a left-back and a centre-back before the start of the Premier League season, with Klopp urging patience as the transfer market kicks into gear with pre-season matches lurking.
England midfielder Alex Oxlade-Chamberlain’s contract stand-off at Arsenal is also being monitored by Klopp, but he has been viewed as a bonus rather than a priority signing.