The Guinea international has established himself as one of the Bundesliga’s top midfield talents over the past 12 months.
And his performances in Leipzig have seen him heavily linked with a summer switch to join Jurgen Klopp at Anfield.
Reports this week have suggested the Liverpool boss is prepared to splash out up to £70m on bringing Keita to England after seeing bids of £57.3m and £66m rejected.
And a sensational claim has now emerged that the Reds upped their offer on Friday night to ensure they get the 22-year-old on-board ahead of next season.
Winner Sports reckon Liverpool have agreed a deal in principle worth a whopping £74.5m (€83m).
They claim the majority of that fee, which would be a club-record, will be paid up front.
Winner Sports claim German sources close to negotiations opened up to them about the prospective move.
They apparently said: "It was in the best interest of all parties to accept this offer."
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Winner Sports add that while the bid has supposedly been accepted, confirmation of a deal depends on the finer details, including payment structure, being approved by Leipzig sporting director Ralf Rangnick and co-owner Dietrich Mateschitz.
The website also claim sources have told them Leipzig are hoping to include a 10 per cent sell-on clause but that the request shouldn’t be an issue as the clubs try to hammer out a deal over the next week.