The likes of West Bromwich Albion, Derby County and Middlesbrough have all seen bids for the 25-year-old rejected, but West Ham had hoped they could entice Forest with an offer.
However, after making contact earlier this week, West Ham have now backed off from the deal having been told of Forest's demands.
The Championship club want £7.5million for the former Sheffield Wednesday man, and that has been enough to put off West Ham - who are now looking at other targets.
Chelsea's Victor Moses is another winger target that remains high on West Ham's wanted list, but HITC Sport understands they want him on loan - whilst the champions would rather sell him.
Slaven Bilic has until 6pm on Tuesday, when the transfer deadline will pass, in which to get any possible deals across the line.