Reports had surfaced through the week that suggested the midfielder could move to Anfield in January, despite having a deal agreed in principle to join next summer.
Questions have been raised about his commitment in Germany following the news that he has already agreed his next move.
Keita and Leipzig have come under criticism this season as they struggle to cope with the demands of Champions League football.
Last season’s Bundesliga runners-up sit bottom of their respective group after a midweek defeat to Besiktas, meaning qualification to the next round is unlikely.
Leipzig, who currently sit sixth in the German top flight, are said to be desperate to keep the midfielder in order to help them qualify for the Champions League for the second successive season.