Coutinho will officially complete his £142m move to Camp Nou on a five-and-a-half-year deal in the coming days after both clubs revealed that they had reached an agreement over his transfer.
The Reds have already brought in Virgil van Dijk for a world-record £75m fee this month, but manager Jurgen Klopp is keen to strengthen further in order to ensure that their top-four challenge does not falter.
The Mirror reports that Liverpool have now identified Lemar as their number one choice to replace the Brazilian after missing out on him towards the latter stages of the transfer window last summer.
The 22-year-old has also previously attracted interest from Arsenal, but Monaco are understood to be unwilling to sell the winger during the January window.
Lemar has scored four goals and set up four more in 20 appearances across all competitions this season.