The NFL and the two teams are scheduled to have an arbitration hearing before the league system arbitrator Stephen Burbank on May 10, NFL Network's Albert Breer reported Wednesday. Such hearings are confidential.
NFL general counsel Jeff Pash on Friday told sports editors during a New York meeting that there was "a high degree of confidence" in the league's case if it goes before the arbitrator, according to The Post.
The teams are accused of creating an unfair competitive advantage by inflating base salary figures for certain players in the 2010, an uncapped year.
Although the teams say there were no rules against dumping large base salaries onto the 2010 books, other franchises were upset about it.
Team owners voted 29-2 in favor of leveling the penalties against the Cowboys and Redskins at a meeting March. The Cowboys and Redskins voted against the punishment and the Tampa Bay Buccaneers abstained.