Sources understands the Reds decided to end their interest when their second, and final, bid was rejected by the Bundesliga club two weeks ago.
It is also understood Liverpool would renew their interest should Leipzig change their stance, but so far there has been no indication that will be the case.
Keita, who scored eight goals in 31 appearances last season, was later pictured making amends with Demme.
Liverpool have made three signings so far this summer, with Mohamed Salah, Dominic Solanke and Andy Robertson arriving at Anfield ahead of the new Premier League season.
