Rush is battling cancer. He is recovering from surgery he had back in March.
The Sun-Times reports Alderman Sandi Jackson is on a short list of possible replacements. If elected, Alderman Jackson and her husband, Congressman Jesse Jackson Junior, would be the first couple in Illinois to represent separate congressional districts.
Congressman Rush released a statement Thursday saying, "last February, the voters of the 1st Congressional District overwhelmingly re-nominated me to serve my ninth term in office...I am and I remain a candidate for re-election in the November general election and look forward to serving the people of my district."
Alderman Jackson says she has no plans to run for Congress.