The Reds were among the clubs who had a serious interest in Lemar in the summer. But it appears that Klopp does not want to spend big money on the French star now.
The Liverpool Echo claim that Klopp has some doubts about whether Lemar can improve the team, given their recent performances in the league and Champions League.
Lemar has not been as impressive at Monaco as he was last season. He only has two goals and eight assists to his name in 25 league games.
Arsenal are now primed to have a second crack at signing the 22-year-old. Last summer, the Gunners had a deadline day move for Lemar fall through at the last minute.