The French international has been the subject of persistent transfer speculation during the last 12 months with his future in Catalonia already decided.
Ligue 1 side Rennes were rumoured to be on the verge of securing a loan deal to bring him back to France before negotiations came to a sharp stop earlier this month.
Rennes boss Bruno Genesio rejected reports of Umtiti failing a medical at the club but doubts have remained over his long term fitness situation.
According to reports from ESPN, via Marca, Olympiakos are ready to open up negotiations with Barcelona over a deal in the coming days.
Barcelona are willing to accept a major loss to remove Umtiti from their inflated wage bill, despite his wage reduction last summer, and they could make a salary contribution in either a loan or permanent exit.