Gamston was chosen by the club as a suitable location for the 45,000-seater stadium, however, the land at the proposed site is owned by the county council and they have refused to support any plans to build on greenbelt land.
County council leader Kay Cutts said Forest acted like a "centre-forward prima donna" by announcing the proposals for the new location on Monday.
"We've made it very clear we would only support a bid on the existing Forest site. Our land at Gamston is not for sale," Cutts told the BBC.
"We don't believe that changing the location of our premier ground is a good move - it's bad for football, bad for business, bad for local people and risks scuppering our bid to be a World Cup city."
Mark Arthur, Forest's chief executive, said exhaustive studies of the existing City Ground had shown it was "impossible to transform the ground into a fully compliant FIFA stadium" fit for the 2018 tournament.