The people said spoke on condition of anonymity because Goodell's decision has not been made public. The commissioner considers it his responsibility to hear the appeal.
The union asked Goodell to withdraw from that role because it said he was not impartial and would be called as a witness.
Brady was suspended for the first four games of the 2015 season after a league-sanctioned report by lawyer Ted Wells found the New England quarterback "at least generally aware" of a scheme to deflate footballs used in the AFC title game.
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