The Hammers are in desperate need of strikers following injuries to Andy Carroll and Andre Ayew and the Frenchman is in their sights.
Remy has been linked with a move to Crystal Palace, but Sky Sports claim West Ham are keen to snatch him from Palace's grasp and have begun negotiations.
Invalid email
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
The Real Madrid midfielder is attracting interest from a host of Premier League clubs and Express Sport understands Chelsea have already submitted a £60m bid.
But Spanish newspaper Mundo Deportivo claim the Reds have joined the race and have made contact with the La Liga giants.
However, the report suggests Liverpool are unlikely to be able to meet Real president Florentino Perez's valuation.