The Reds have already had a transfer proposal turned down by Leipzig for the Guinean midfielder but Klopp has once again proven his keenness to bring Keita to Anfield.
The Times reported that Klopp has told the club to accelerate their pursuit of the 22-year-old.
However, they will have to break their transfer record for a second time this summer with Leipzig now demanding £80 million for the midfielder. Liverpool broke their transfer record by signing Mohamed Salah for £37 million already this transfer window.
The report further suggests that Keita is expected to meet Leipzig’s Oliver Mintzlaff and the rest of the management board this week to determine where his future lies.
The Kornaky-born midfielder was impressive throughout the season for Leipzig and scored eight times in 30 appearances last season which sent an alert to a number of clubs across Europe’s top leagues.