Arsenal saw a £92m offer accepted for the 21-year-old winger on Thursday afternoon as they sought a replacement for the Manchester City-bound Alexis Sanchez.
Lemar, however, turned down the opportunity to move to the Emirates, with Anfield said to have been his preferred destination.
Arsenal subsequently blocked Sanchez’s move to the Etihad, thereby risking that they would lose him on a free transfer when his contract expires next summer.
Any deal for Lemar was complicated by the fact that he was in line to start in France’s World Cup qualifier against the Netherlands in Paris on Thursday night.
After scoring twice in a 4-0 victory for France, Lemar claimed that he was committed to Monaco despite the earlier uncertainty over his future.
“I'm a Monaco player, I'm very happy there. Now, I'm going to have a good season with my club, try to improve and move forward in my career. I am going back to Monaco,” Lemar told Canal+ Sport.
“I prepared for this game as I usually would. I don't get carried away, even if there is the transfer window. I was focused on my match, that's all that counted for me.”
Had he moved, Lemar would have been the fifth member of the Monaco side that reached last season’s Champions League semi-finals to leave the club in a high-profile move this summer.
Benjamin Mendy and Bernardo Silva joined Manchester City for a combined total of £95m, while Chelsea paid a reported £40m for Tiemoué Bakayoko.
On Thursday, Kylian Mbappé joined Monaco’s Ligue 1 rivals Paris Saint-Germain in a loan deal which could be made permanent for a fee of £165.7m.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies