Fryatt is out of contract at Hull and he turned down an improved offer from the Tigers last week to stay at the KC Stadium.
The news alerted Forest and they are in pole position to land the former Leicester City man after stepping up their interest.
Forest boss Stuart Pearce is desperate to bolster his attacking options after seeing a number of forwards leave the club at the end of last season, and he has made Fryatt one of his top targets.
Several Premier League and Championship sides are thought to have expressed an interest in signing Fryatt, but Forest are hoping to steal a march on their rivals by luring him to the City Ground.
Despite seeing Premier League action limited with the January arrivals of Shane Long and Nikica Jelavic, and despite not starting a Premier League game all season, Fryatt was still the club's top goalscorer in all competitions last term with six goals to his name.