The 21-year-old did not play a single minute of action under former Reds boss Arne Slot last season after returning from loan spells at RB Salzburg and Las Palmas in 2024/25.
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Andoni Iraola has assessed him over the summer, as the Galicia-born playmaker is now back up to full fitness, but he does not feature in the Basque coach's plans moving forward.
Transfer guru Fabrizio Romano has now revealed talks are advanced for him to rejoin Celta Vigo as talks over personal terms continue.
Bajcetic spent seven years in Celta's youth set up, before moving to Liverpool in 2013, and a move back to Spain could reignite his stalled career after a difficult few years on Merseyside.