The ECHO understands that the France international is not on the list of targets under consideration ahead of this summer's transfer window.
Lemar has been heavily touted as a potential replacement for Philippe Coutinho, who was sold to Barcelona for £142million in January.
Reports in France this week suggested that Liverpool's hopes of signing him had been bolstered by his refusal to pen a new contract.
However, the Reds are no longer pursuing the 22-year-old and are focusing their attention elsewhere.
Sporting director Michael Edwards held talks with Monaco last August but the Reds were unable to agree a deal with the Ligue One outfit.