Warnock was widely expected to be named as the replacement boss until the end of the season, although a source close to the manager has now claimed that he has turned the club down.
The 65-year-old has been out of management for almost a year, having been sacked by Leeds on April 1, 2013 with the club just five points above the relegation zone.
He also has previous experience working in Nottingham having spent four years in charge of Notts County earlier in his career.
"I did not feel the conditions of the job were right for me to manage. I wish them well for the rest of the season," Warnock is quoted as saying by The Independent.
Forest are now without a win in eight matches in all competitions and sit two points outside the top six in the Championship table.