But Mundo Deportivo claim Klopp still retains an interest in signing Traore.
Barcelona have also been linked with bringing the attacker back to Spain and Traore has given his thoughts on a potential move.
“We talk about everything, more general topics because I have been at the club for many years and so has he,” Traore said.
“We met in the academy, we spoke about things to do with the team, the things that we have happened together at Barcelona and we know each other well.
Traore would certainly give the likes of Mane and Salah a run for their money in a sprint race.