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.
His move to Al-Ittihad had appeared to be closing to completion, but has now been held up by paperwork, with both parties looking to resolve the issue.
Fabinho would like to bring his beloved French bulldogs with him to Saudi Arabia, although he may be affected by the country's strict dog rules.
The breed are classified as 'dangerous and aggressive dogs' in Saudi Arabia and are generally not allowed in the country, although this is not a major issue in holding up the deal.
Jordan Henderson is another midfielder headed for the door at Anfield, as he is set to join Steven Gerrard's Al-Ettifaq for £12m after reportedly completing a medical on Saturday.
The Reds have already bolstered their creative options by signing Alexis Mac Allister from Brighton for £35m and Dominik Szoboszlai from RB Leipzig for £60m.
However, with two key players likely to leave the club this summer, Jurgen Klopp has admitted that more players will need to arrive before the transfer window closes.
'There are so many things to do, he said, speaking on the club's 'We are Liverpool' podcast. 'The transfer window is open. If my day would have 28 hours at the moment it would not be a problem - I could fill them easily!
'Still three-and-a-half weeks until the first game of the season. A few things have to happen before then, definitely, transfer market-wise as well. That is clear now. And it will happen. New players have to come in. We will have a good team.'
Multiple midfield options have been linked with Liverpool.
There has been speculation surrounding a swoop for Southampton's 19-year-old starlet Romeo Lavia, but his £50m price tag could deter them considering his relative inexperience.
The club are also costing up a move for Crystal Palace man Cheick Doucoure. The south London side have slapped a £70m valuation on the Mali international but are yet to have their resolve tested by a bid.
Earlier in the summer, it looked as if their interest in Nice's Khepren Thuram had cooled after acquiring Szoboszlai, but the departures of Henderson and Fabinho could revive that.