Forest are on the hunt for a new goalkeeper, with Karl Darlow's departure to Newcastle United leaving them short of numbers in that position.
At the moment Dorus de Vries is their main senior option, with Dimitar Evtimov set to be used as cover, but Dougie Freedman would like to add more quality.
There are doubts over whether De Vries and Evtimov could become first-choice stoppers for the entire season and, as a result, the Reds are on the hunt for a new addition.
They reportedly feel that Foderingham would be good buy after his stellar showings for Swindon over the past few seasons.
Foderingham has impressed at League One and League Two level and he has developed a reputation as one of the finest stoppers in the Football League.
It means that Swindon will not want to lose him, but the Robins have already cashed in on two of their key stars - with Massimo Luongo and Ben Gladwin joining Queens Park Rangers - and Foderingham could follow suit, if Forest table a good offer.
Signing the goalkeeper may not be straightforward, though, as the Mirror also say that Birmingham City are set to lodge a bid for Foderingham.