Lemar rose to the attention of the footballing world last season after scoring nine goals for Monaco as they took the Ligue 1 title.
Arsenal were linked with a swoop for the talented midfielder, who has also been capped 10 times by France, but the Reds were also said to be keen on the youngster.
However, the Liverpool Echo claim Klopp does not feel the Guadeloupe-born star would add to his attacking talents, despite losing Philippe Coutinho to Barcelona in January.
Monaco vice-president Vadim Vasilyev seems convinced that Lemar will be on his way at the end of the season, however, telling reporters after their defeat to Paris Saint-Germain at the weekend: ‘A few hours of the match against Paris is not the time to talk about the transfer window. But good luck to those who want him.’
Massimiliano Allegri says Juventus still have the advantage in the race for the Serie A title this season.