Upton Park boss Slaven Bilic has stepped up his interest in the 25-year-old in the last few days after bids for him from Derby and West Bromwich Albion were turned down earlier this month.
But talks have broken down and sources close to the player are not confident a deal can be struck ahead of the transfer deadline.
Antonio scored 15 goals for Forest last season and continued interest in him led to manager Dougie Freedman withdrawing him from the squad which played Charlton on August 18.
Freedman claimed the winger was not in the right frame of mind to play but he consequently returned against Bolton four days later and scored against Cardiff on Saturday.
Antonio signed for Forest from Sheffield Wednesday on a free transfer last summer after two successful years at Hillsborough, where he scored 13 goals in 70 appearances.
He began his career as a Reading trainee and had spells on loan at Cheltenham, Southampton and Colchester before his most successful loan period at Wednesday was made permanent in 2012.
Antonio has expressed a desire to play in the Premier League but his chances of doing that in the immediate future are currently fading.
Forest, meanwhile, are close to agreeing a deal with Brighton over a loan move for striker Chris O’Grady.
The forward has featured in five matches for his club this season but is yet to score after four goals last term.
Lille’s Ryan Mendes, a Cape Verde international, is someone who could also end up at the City Ground. The two clubs are in negotiation about a possible loan deal.