The Hammers hitman is surplus to requirements at the London Stadium and passed a medical in France yesterday.
But his £9m switch to Rennes was thrown into doubt when Palace came in with a £10m offer for the 27-year-old.
West Ham have yet to sanction his sale but Sakho is out of contract next summer and has hardly played over the last few months.
Palace are trying to add to a strikeforce heavily reliant on Christian Benteke and see Sakho as a good option.
But the player was on the verge of accepting a move to Rennes before they made their move and talks are set to continue today.
West Ham have made a move for Ghana forward Abdul Majeed Waris, who was relegated from the French top flight with Lorient last season.
Waris, who can play up front or on the left wing, is in London for talks after rejecting an £8m move to Burnley.
