The Japan international, 31, joined Liverpool on a four-year deal from Stuttgart for around £16.2m last August.
In his debut season at Anfield, he made 43 appearances, including 20 Premier League starts, and won the League Cup.
Marseille, managed by Roberto de Zerbi, who faced Endo as Brighton boss last season, made the offer.
The Reds are also aware of additional interest in the defensive player from other German clubs.
Liverpool have yet to make a signing this summer following the arrival of manager Arne Slot.
