Lyon travel to Strasbourg next weekend before hosting Nice on the final game of the Ligue 1 season, with the club looking to secure a runners-up position in the top-flight of French football.
Klopp was quizzed on the reports after the Chelsea loss but curiously did not deny each claim entirely.
Liverpool have not agreed a deal to sign Lyon midfielder Nabil Fekir despite reports to the contrary, according to a reliable journalist.
Klopp recently said he is planning to improve the depth within his Liverpool squad this summer, but sources said no move is imminent regarding Fekir.
While the Reds were in Premier League action against Chelsea on Sunday, reports in France emerged suggesting that a deal had been done for Fekir.
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Fekir would certainly fit into Liverpool's attacking style of play - having scored 22 goals and produced eight assists from midfield for Les Gones so far this season. I would be surprised about that.
He said: "We have had no contact with Liverpool today".
But Klopp, who usually stays silent on transfer speculation, did respond when he was asked about Lyon captain Nabil Fekir. "At the end of the season, we'll see, but for the moment, there's nothing".
"If that is the case [that he is joining] we would be really happy to have him at our home", Mane continued.