Lemar had formerly been a target of Arsenal in the summer transfer market, but Liverpool have gone ahead with formal interest in the final hours before Thursday night's deadline.
Information relayed by RMC in France suggests that the purpose of the meeting was to thrash out a deal for Lemar, who is now seen by the Reds as a primary target.
Lemar joined Monaco from Caen in 2015 and enjoyed a stunning season in 2016/17 as the club captured a first French title since 2000 and reached the last four of the Champions League.
The 21-year-old also scored 14 goals in total from his attacking midfield/wide forward role.
Liverpool fans may be wondering if moving ahead with, and possibly signing, Lemar will come as a result of the Reds attempting to replace Philippe Coutinho, who continues to be a serious target for Barcelona.
But Spanish football expert Guillem Balague has claimed that any further talks regarding potential Liverpool signings remain independent of the Coutinho saga. That means Lemar may not hinge on the Brazilian's departure and both could be playing for Liverpool this season.
Coutinho: LFC's signings/negotiations independent of his future. They insist they not selling. No new FCB offer has arrived at this point pic.twitter.com/RMbzfoskCJ— Guillem Balague (@GuillemBalague) August 30, 2017
It remains Liverpool's intention not to sell Coutinho after rejecting multiple enormous bids.