There is an expectation that the case will be resolved within the next 48 hours, and ESPN's Stephen A. Smith is hearing that NFL commissioner Roger Goodell likely will uphold the suspension stemming from Brady's involvement in the Deflategate scandal.
The reigning Super Bowl champion Patriots open training camp Thursday.
If the suspension is upheld, it is widely expected that Brady, who reported to camp Monday, will go to federal court and seek an injunction that will allow him to play while his case works its way through the courts.
The NFL Players Association has been trying to reach a settlement on the Brady case -- an attempt that originally was met with "silence" by the NFL, sources confirmed to ESPN.
The league ultimately responded, and the sides have engaged in talks in recent days, although sources told ESPN that it is unlikely a settlement will be reached.
Brady, according to sources, remains adamant that he will not accept a suspension and that any punishment must specify that it's for failing to cooperate with an NFL investigation and not for breaking rules with the footballs.
Brady was suspended for the first four games of the 2015 season on May 11 after Ted Wells' investigation found that it was "more probable than not" that Patriots personnel deliberately deflated footballs during the AFC Championship Game and that Brady was "at least generally aware" of the rules violations. The Patriots were fined $1 million for the infraction.
Brady appealed his suspension, and Goodell heard the appeal on June 23 after refusing NFLPA requests to recuse himself as the appeals officer.
Will a settlement be reached in Brady appeal?
Adam Schefter discusses whether the NFL and NFLPA will agree to a settlement in QB Tom Brady's appeal of his four-game suspension.