The 21-year-old right-back joined on a two-year loan deal last summer and made 19 appearances, but he did not play a single Premier League game after December.
Reds boss Brendan Rodgers has recently signed two new right-backs; Nathaniel Clyne from Southampton and Joe Gomez from Charlton – and is considering his options as he reshapes his squad.
He has also handed a new long-term deal to young right-back Andre Wisdom and Sky sources reported at the end of last month that England U19 international Gomez is also under consideration for a loan.
The Liverpool Echo report Manquillo would not be averse to the idea of moving on, either back to Atletico or to another club.
Manquillo made 10 Premier League starts in the first half of last season. He made nine first team appearances for Atletico prior, having made his way through their youth ranks.
He has also represented every level of Spain’s youth system from U16 to U21, but is yet to appear for the seniors.