The Saints placed their exclusive rights tag on Brees earlier this offseason and Brees' first team, the San Diego Chargers, placed the tag on Brees in 2005 after his rookie contract expired.
The sources said the union is seeking a decision and/or clarification regarding the league's policy that stipulates a second franchise tag is a 120 percent bump from the first tag and the third time is 144 percent.
Brees' current tag is worth $16.371 million. According to ESPN.com senior NFL writer John Clayton, a 144 percent bump would put Brees' cap number at $23,574,240, though an exclusive tag could raise the number a little higher. That would put his two-year earnings at $39,945,240, a little less than $20 million a year.
The Saints and Brees are locked in a protracted contract battle and the sides have until July 16 to hammer out a long-term extension.
The applicable language in the collective bargaining agreement says "any club that designates a player for the third time ..."
The union's position is the CBA intended for a player to be franchised no more than three times.
Information from ESPN.com senior NFL writer John Clayton and The Associated Press contributed to this report.