The NFL declined to comment to Breer.
Brady, who was hit with the penalty following an investigation into his involvement with improperly deflated footballs used in the AFC Championship Game, is still slated to have his case heard by Commissioner Roger Goodell. The union previously asked that Goodell recuse himself as arbitrator in Brady's appeal.
The suspension hearing is a separate matter from the penalties levied against the Patriots organization, which included a $1 million fine and the loss of a 2016 first-rounder and a 2017 fourth-rounder. Patriots owner Robert Kraft said the team would "reluctantly" accept those penalties in a recent news conference.
Goodell had said Kraft's acceptance of those penalties will have no bearing on the outcome of Brady's appeal.
Should the four-game penalty stand, it will remove one of the league's most popular players for the first quarter of the NFL's regular season. Brady just won his fourth Super Bowl title and made his sixth appearance in the game since entering the league in 2000.
In that time, Brady has been a picture of stability for the franchise, with the 2008 season being the only one during which he missed significant time (he tore his ACL in the season-opener).