The Daily Mirror is reporting that the Merseyside outfit are ready to return with a fresh bid for the 22-year-old midfielder after having had a £66m offer rejected this week.
The same story says that Liverpool will make their next decision on their bid to sign the Guinea international next week as Klopp looks to strengthen his squad ahead of next season.
The article says that Keita has a buyout clause of £50m in his current contract but that does not come into effect until next summer.
Liverpool are believed to be on the lookout for a number of new signings as Klopp prepares for his second season in charge at the Merseyside outfit.
The Reds have so far concluded deals to land striker Dominic Solanke and winger Mohamed Salah so far this summer.
Liverpool are gearing up for a return to the Champions League next season after the Reds finished fourth in the Premier League table last term.
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