Fabinho remains keen on joining Saudi Pro League side Al-Ittihad after the move was held up by a paperwork issue.
The 29-year-old is expected to leave Anfield this summer and had been in talks with the Saudi Pro League over a £40 million switch, although Bayern Munich also remain interested.
If he does leave the club, it will end a successful five-year spell at Anfield that saw him win five major trophies.
The Brazil international racked up over 200 appearances for the club, and could leave a considerable hole in the Reds midfield.