The Reds had hoped their improved offer for the Guinea international would have secured a breakthrough in discussions with the Bundesliga outfit.
However, it was dismissed out of hand and Liverpool are left facing the prospect of missing out on Jurgen Klopp's top summer target.
Keita is desperate to move to Anfield but Leipzig's position appears so entrenched that agreeing a deal this summer looks increasingly difficult.
Even the player submitting an official transfer request appears unlikely to break the deadlock unless Leipzig back down.
Liverpool must decide whether to table a third offer in excess of £70m having failed with bids of £57m and then £66m.
Sources close to the club have distanced themselves from reports that Keita's agent has flown out to Hong Kong for talks with the Reds.
Liverpool sporting director Michael Edwards didn't travel on the tour and remains in the UK.
Edwards is in charge of all transfer discussions as the Reds look to wrap up the signing of Hull City left back Andy Robertson and sell Kevin Stewart in the opposite direction.
Unless Leipzig's stance changes soon then Liverpool will have to look at alternative options to Keita.
Source: Liverpool Echo
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