Mario Balotelli is being linked with a stunning move away from the club this month, with Greek side Olympiakos interested.
The striker has yet to score a Premier League goal and even manager Brendan Rodgers has admitted his style is not a great fit with his own philosophy.
Italian website TMW report Greek champions Olympiakos are keen to sign Balotelli on loan, and are preparing an offer.
The deal would include €2.5 million up front to help tempt Liverpool to sanction the move.
From Liverpool's end, it could depend on their success in rumoured attempts to bring in Divock Origi and end his season long loan at Lille early.
It may be better however for them to try to cut ties with the Italian international permanently if they are prepared to do so, and if such an offer does not arrive then they may be better off keeping the controversial striker to see if he can improve.