The Reds have seen bids of £57m and £66m turned down by the Bundesliga club already this summer, but reports surfaced earlier today suggesting that they would return with a third and final offer.
However, the Liverpool Echo claims that is not the case and that the club have decided to look at other targets due to Leipzig's insistence that they will not sell.
Liverpool will reportedly only reignite their interest if Leipzig perform a U-turn and soften their stance on the 22-year-old, who is understood to be keen on the move himself.
Jurgen Klopp's side are planning to return for the Guinea international next summer, however, when it is believed he can move for his release clause of £48m.
Keita made 31 appearances last season as Leipzig finished second in the Bundesliga table.