The Reds have even explored the possibility of trying to sign Naby Keita six months earlier than expected - something that his club RB Leipzig are determined not to let happen.
However, it looks like Liverpool have now emerged as the front runners as the Mirror claims that Lemar is ready to snub interest from the likes of Arsenal and Chelsea as he's keen on making a move to Anfield.
Coutinho bagging a whopping £142 million from Barcelona has motivated Monaco to sell their stalwart for a maximum price as they feel they can squeeze a good amount from the Lemar deal.
Arsenal are visibly feeling the pressure, and have turned towards Thomas Lemar.
Liverpool - as well as Arsenal - were heavily linked with a swoop for Lemar in the summer window but a deal never materialised.
"Monaco's position is that they don't intend to sell any of their top players this month. We wait until the summer because we feel that's not the right time for us to sell".
Liverpool will reportedly not move for Lemar this month.
Lemar is regarded as one of the most exciting young midfielders to have emerged out of France in recent years, thanks largely due to his exploits for Monaco last season.
The Gunners looked certain to land the mercurial France global after what would have been a club record fee was agreed.
The France defender has been just a bit-part player at the Emirates under boss Arsene Wenger this season. But it also makes a lot of sense as to why Lemar would want to wait, why Monaco would want to wait.