Leipzig had initially taken a hard stance to the move, denying that they had any need to sell him.
But it appeared that headway had been made this weekend, with suggestions that Keita would line out for Leipzig for the final time against Schalke on Saturday evening before heading to Liverpool to finalise his deal.
Having said that, the Liverpool ECHO reports that there is no agreement in place yet after initial discussions between sporting directors Michael Edwards and Ralf Rangnick failed to produce anything concrete.
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The claims arrive after it emerged Keita has registered a company in the UK.
Williams' information has however tied in with news that Keita registered a company named "NK8 Limited" - with him as the director and the location in the United Kingdom - earlier this week.
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Liverpool are willing to pay an additional premium to sign the player early but Leipzig are trying to convince him to stay until the end of the season to help them secure Champions League football and possibly a decent placing in the Europa League.
That's not going to cut it with the Liverpool fans will are desperately searching for any hint he will arrive in January.