Jackson, 47, disclosed this summer he was being treated for depression and has undergone weeks of hospitalization.
Jackson campaign consultant Kevin Lampe said Thursday the lawmaker remains under medical care, the Chicago Tribune reported.
"As soon as the doctors say he can get back to work, he'll get back to work, which includes campaigning," said Lampe.
Jackson leads his challengers -- Republican Brian Woodworth, 41, and Independent Marcus Lewis, 53 -- in polls, the newspaper said.
DePaul University political scientist Wayne Steger said the challengers would need to give voters a reason to reject a 17-year incumbent, and then "would pretty much have to bombard people with advertising, fliers and mass mailings. It would take a sustained bombardment of publicity."