Norman said the league told him the fine had more to do with having the words "proud, brave" written on the side of the cleats than the red, white and blue colors that didn't match Carolina's color scheme as required.
"We're appealing it," Norman said. "I appeal everything, doesn't matter what it is."
Norman was fined $11,000 last season for wearing predominantly silver cleats in a game against the Minnesota Vikings. He got half of that back on appeal.
He is giving the cleats, which he has autographed, to the USO of North and South Carolina for an online auction. Money raised will go to help troops at Fort Jackson in Columbia, South Carolina.
Norman is a native of Greenwood, South Carolina.
"Just give that back to them and give them hope and let them know we care about them and love them as well," Norman said.
Carolina coach Ron Rivera was asked Wednesday if the league should have made an exception on the fine because Norman was honoring the troops in a game that was about honoring the troops.
"That's not for me to say," said Rivera, whose team is 8-0 heading into Sunday's game at Tennessee. "What will happen is Josh will work something out with the league. It's one of those things we've got to be smart about what we do."