Fabinho has been left out of Liverpool’s squad for a training camp in Germany following a £40m bid for him from Saudi Arabian club Al-Ittihad.
Liverpool captain Jordan Henderson has also been linked with a move to Saudi Arabia but has travelled to Germany.
The Reds received the offer for Brazil midfielder Fabinho on Friday night.
A decision between the club and player was then taken to remove the 29-year-old from the 32-man touring party, which left on Saturday.
Fabinho has been at Liverpool since July 2018 after the Reds signed him from Monaco for a fee in the region of £39m.
He has since helped the club win the Premier League, Champions League, FA Cup, League Cup and Fifa Club World Cup.
There are reports Henderson is a target for Al-Ettifaq, who recently appointed former Liverpool captain Steven Gerrard as their new manager.
Liverpool have not set an asking price for the 33-year-old but the £10m offer being speculated about falls well below the club’s valuation for a player with two years left on his contract and who has been an integral part of their side.
The Reds have already been rebuilding their midfield following the departures of James Milner, Naby Keita and Alex Oxlade-Chamberlain.
They have signed Argentina international Alexis Mac Allister, 24, from Brighton and Hungary captain Dominik Szoboszlai, 22, from RB Leipzig and were looking at long term successor to Fabinho.
Southampton midfielder Romeo Lavia, 19, was one of those under consideration but if they lose the experience of Fabinho, and possibly Henderson, it is expected to see the club shift their transfer strategy.
A number of potential targets are believed to be under consideration but Brighton midfielder Moises Caicedo, who is expected to join Chelsea, is not one of them.
The player exodus to Saudi Arabia
Fabinho would be the latest in a number of big-name players to move to Saudi Arabia this summer if his transfer goes through.
His former Liverpool team-mate and compatriot Roberto Firmino, whose contract with the Anfield club had expired, has joined Al-Ahli, who also signed Senegal keeper Edouard Mendy from Chelsea.
Al-Ittihad, meanwhile, have already brought in former Real Madrid striker Karim Benzema, ex-Chelsea midfielder N’Golo Kante and Portuguese forward Jota from Celtic.
Al-Hilal have signed Portugal midfielder Ruben Neves from Wolves and Senegal defender Kalidou Koulibaly from Chelsea.