The Daily Mail says Crystal Palace have made a last-ditch £10m bid for his services.
The Hammers will now have to decide whether to sell Sakho to their London rivals or accept less and allow him to move abroad.
Sakho is closing on a £8million move to Rennes after passing a medical.
He told Sky Sports: "I have had a frustrating time for the past couple of seasons. I want a fresh start and I want to get back to playing regular football."