The 29-year-old had been in talks with Fulham in January, and they had won a work permit for him.
Boateng himself was at the Africa Cup of Nations with Ghana - but he had hoped a move to England would finally happen, having previously seen a move to Middlesbrough collapse earlier in his career.
Boateng has been playing for Dnipro in Ukraine, but he has been in dispute and had looked to take his case to the Court of Arbitration for Sport to try and secure his release from his contract.
However, with the Fulham deal faltering - Olympiakos have now stepped in and are looking to push through a move.
Sky Sports understands that Boateng himself is now in Greece undergoing a medical with the Athens outfit.