The Jackets waived Campbell last week after they could not work out a trade for the veteran center. When he went unclaimed, he was assigned to the AHL.
But his agent said Campbell, 32, chose not to report rather than take a roster spot from a younger player.
"He's going to continue to skate on his own and ponder his future," Pat Morris of Newport Sports Management told the Columbus Dispatch.
"He was a young player at one point in time, and older players didn't come in and take his position away. He doesn't want to do that."
By not reporting, Campbell is forfeiting his $1.3 million salary.