The Reds have been regularly linked with a move to sign the France international over the past eight months or so.
Indeed, Liverpool FC were thought to be Lemar’s first-choice destination in the summer after Arsenal agreed a £92m fee with Monaco but the player turned down a move to the north London side.
Klopp has transfer funds to spend in the January transfer window after Liverpool FC sold Philippe Coutinho to Barcelona in a £142m deal at the weekend.
The Merseyside outfit have been linked with a fresh move to sign Lemar, although the French attacker would be cup tied in the Champions League ahead of their last-16 clash against FC Porto next month.
French football expert Laurens believes Klopp would transform Lemar into a world-class player at Anfield.
“For all Liverpool fans it is a given that he is going to come and replace Coutinho as early as this month,” Laurens told BBC Sport.
“Right now, Monaco have received no offers from Liverpool or Arsenal, or anyone else. In the summer he was definitely closer to joining Arsenal than Liverpool.”
Laurens added: “But as much as I would love him to go to Liverpool because he would suit this team perfectly – he can play in different positions; he is so good on set pieces; his left foot is amazing – I think Klopp would make him even more world class than he already is.”
Lemar scored 11 goals and made 11 assists in 48 appearances in all competitions for Monaco in the 2016-17 season.
The France star helped Monaco to pip Paris Saint-Germain to the Ligue 1 title and reach the Champions League semi-finals.
Liverpool FC signed Virgil van Dijk in a £75m deal from Southampton last week.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news