According to The Independent, Jurgen Klopp has a long-lasting interest in the France international and will look to beat Arsenal to his signature next month.
Such is Liverpool's interest in Lemar they will go through with the move for the 22-year-old whether Coutinho completes his move to the Nou Camp or not.
Sport claims Coutinho will agree a €12m-a-year deal to move to the Catalan giants, taking the total cost of the transfer to an eye-watering €210m.
Arsenal came tantalisingly close to signing Lemar on the final day of the summer transfer window in August, but the deal eventually fell through.
Among the reasons for the collapse of the transfer – which also led to Manchester City missing out on signing Alexis Sanchez from The Emirates Stadium club – was the player's desire to feature in the Champions League.
And while the Gunners are stuck in the Europa League and outside the Champions league places in the Premier League, Liverpool have reached the round of 16 in Europe's premier club competition and are fourth in the top flight.
Lemar is thought to therefore prefer a move to Liverpool over fifth place Arsenal though Monaco are likely to demand upward of £90m for the wideman, whose 2017-18 campaign has been dogged by injury.
The Guadeloupe-born player has made just 17 appearances in all competitions for the side from the principality, who are second in Ligue 1, nine points behind runaway leaders Paris Saint-Germain, and finished bottom of their Champions League group after failing to win any of their six matches.
Monaco resisted offers for Lemar in the summer due to wanting to sustain the success which saw them beat PSG to last season's French title, but they were powerless to prevent Benjamin Mendy, Bernardo Silva, Tiemoue Bakayoko and Kylian Mbappe departing for pastures new.
Alongside Joao Moutinho and full-back Fabinho he remains one of the few star players to have remained at Monaco, but his days with the club are seemingly numbered as he seeks to force his way in the star-studded France squad for next summer's World Cup finals in Russia.