The Hammers are now short of options in the final third of the field, having allowed Sebastien Haller to join Ajax on a permanent deal.
The report claims that the 27-year-old, who was linked with West Bromwich Albion last summer, would be open to a switch to the English capital for the second half of the season.
Diaz has been involved in seven first-team matches for Madrid this term, including their last two in La Liga, contributing one goal for Zinedine Zidane's side.
The Dominican Republic international has found the back of the net on 11 occasions in 47 appearances for Los Blancos in all competitions. body check tags ::