The 20-year-old was sent out on loan to French side Lyon for the second half of last season as he struggled for regular minutes at Real Madrid under Xabi Alonso and Alvaro Arbeloa.
Endrick caught the eye during his time in Ligue 1, scoring eight goals and providing eight assists in his 21 games across all competitions, before heading back to Madrid in June for preseason.
Liverpool reached out over a loan package for the full 2026/27 season, but that was rejected, as Jose Mourinho wanted to assess him on his return from injury.
The former Palmerias attacker is due back in match action from October, but if chances are still limited, Mourinho may reconsider his position in the mid-season market.
Liverpool remain open to a loan, but they face a battle with AC Milan, who can offer more opportunities after the departure of Rafael Leao to Galatasaray.