No official bid has yet been made but the Anfield club have a strong interest in the 18-year-old centre-back.
Arsenal, Aston Villa and Spurs have also been watching Gomez, a player Charlton value at up to ??7m.
Gomez played 24 times for the Addicks last season and has also represented England at U16, U17 and U19 level.
The Catford-born player was part of the England side that won the 2014 European U17 Championships and was named in UEFA’s team of the tournament.