The Champions League finalists are on the lookout for a long-term successor for Jordan Henderson and James Milner in midfield.
After capturing the eye of Monaco and the France national team over the last 18 months, the 22-year-old is regarded as one of the top young prospects in the world.
Tchouameni has a contract with Monaco until 2024, but the French club is planning to sell him, even if it would cost more than £50 million.
Declan Rice is a major fan of Jurgen Klopp’s, but West Ham’s £100 million price tag is out of reach for Liverpool.
Tchouameni has a wealth of experience, having made 131 senior games for Bordeaux and Monaco.
He has eight France caps and one international goal to his record, as well as a UEFA Nationals League trophy.
Milner, 36, is out of contract at the end of the season, but he remains a key player for Klopp, having made 36 appearances in all competitions.
Henderson, 31, is still a key player, although he has been left out of the starting lineup in recent games against Everton and Villarreal.