Briggs, 30, said he is not immediately looking for a trade, but if his pay isn't boosted, he may revisited the idea, the Chicago Tribune reported.
"I'm going to go out and play the game the way I've always played it and see what happens," Briggs told the Tribune Sunday. "I'm going to plug away and do what I've always done. I'm here to help us win a championship."
Briggs and agent Drew Rosenhaus approached the Bears about restructuring the player's pay deal. Currently, Briggs' six-year $36 million deal reached in 2008 states he cannot receive more than $21.6 million within the first three years.
Briggs is scheduled to make $3.9 million this season, which is low compared with other younger and less proven linebackers across the country. A.J. Hawk of the Green Bay Packers will make $10.5 million this season, while the Jets' David Harris will pull in $29.5 million over four years.
"I'm happy to see everybody make their money around the league," Briggs said. "I want everybody to be successful. My circumstances are different. That's all I can really say."