The Monaco sensation has been heavily linked with a move to the Premier League in recent months.
Liverpool and Arsenal were in for the France international in the summer, with Manchester United also tracking the highly-rated winger.
Both the Gunners and the Reds tabled bids for the 22-year-old but Lemar opted to stay in Ligue 1.
And according to Yahoo Sport, Lemar has decided to snub interest from United and Arsenal to join Liverpool.
They claim the Monaco ace has held talks with the Reds and told the club he wants to move to Anfield.
GETTYThomas Lemar has agreed to join Liverpool
“Thomas Lemar has agreed to join Liverpool”
Yahoo Sport add that Lemar would be a replacement for Philippe Coutinho, who is set to join Barcelona.
Starsport understands Coutinho feels he’s played his last game for Liverpool under Jurgen Klopp.
Barcelona made three bids for the playmaker in the summer, who handed in a transfer request in hope of securing his dream move to the Nou Camp.
However, the Reds stood firm and kept hold of their star man.
Coutinho has been in fine form this season.
The Brazil international has netted 12 goals and chipped in with eight assists in all competitions under Klopp.
Liverpool are back in action on Friday night when Klopp's men host Everton in the FA Cup third round at Anfield.
However, Coutinho is expected to be absent for the Merseyside derby, with talks over his move to Barca ongoing.