"I don't have a thing to say about that," Brown said while attending the NFL Fall Meeting, adding that he doesn't like to comment on football matters.
Palmer is currently out of football, holding true to his pledge to retire if he isn't traded. Brown hasn't given in to Palmer's demand and said during the preseason that the Bengals consider the quarterback to be retired.
The Bengals retain Palmer's rights since he is under contract, meaning he can't play for another team unless he is traded or released.
The league's trade deadline is Tuesday, Oct. 18.
In Palmer's absence, the Bengals are off to a 3-2 start behind rookie quarterback Andy Dalton, who has led the team to fourth-quarter comeback wins in each of the last two weeks, against the Buffalo Bills and Jacksonville Jaguars. He has thrown for 1,047 yards and six touchdowns with five interceptions.