Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
Mark Hughes insists Stoke will not be looking to make any major additions in the January transfer window.
As revealed on Friday, Forest were poised to sign Gillett on a free transfer after he impressed on trial.
Gillett left Doncaster earlier this summer upon the expiration of his contract at the Keepmoat Stadium.
The 26-year-old has penned a two-year deal at the City Ground after being reunited with former Rovers boss Sean O'Driscoll.
Gillett is Forest's fifth signing of the summer and Forest chairman Omar Al Hasawi was delighted to land the midfielder.
"Simon is a player that Sean knows well from his Doncaster days and we are delighted to welcome him to the club," Al Hasawi told the club's official website.