According to reports, the Reds see Upamecano as a potential alternative to Crystal Palace defender Marc Guehi, who is also out of contract in June.
Unlike Guehi, Liverpool can pursue a pre-contract with Upamecano from January 1, as there are no restrictions on signing players from other countries.
Real Madrid are also reportedly interested in Upamecano, but Liverpool may try to secure his services early by making an offer in January.
The Reds are facing defensive concerns after losing Giovanni Leoni to a season-ending knee injury.