French outlet Le10Sport, as quoted by the Daily Express, is reporting that the Reds are ready to make a move to sign the 21-year-old midfielder, who has regularly been touted as a target for Arsenal this summer.
Arsenal, though, appear to be struggling to get a deal over the line to bring Lemar to the north London side.
The same report claims that Arsenal are thought to have had an offer of around £50m rejected by Monaco, who appear determined to keep hold of the France international.
Now, it is claimed that Liverpool are ready to join the race for the signature of the attacking midfielder, as Jurgen Klopp prepares for his second full season in charge at Anfield.
The same story says Liverpool are making plans in case they lose Philippe Coutinho to Barcelona this summer, and Lemar has emerged as a potential target for the Merseyside outfit.
Liverpool have signed three players so far this summer after having tied up deals for Mohamed Salah, Dominic Solanke and Andy Robertson.
Klopp is likely to want further reinforcements, however, as Liverpool prepare for a return to the Champions League next season.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news