In announcing the special election on his Twitter page Monday, Quinn also posted, "I will work with lawmakers to move the general election to Apr. 9, which will save money by coinciding with local elections."
Jackson resigned last week.
Former U.S. Rep. Debbie Halvorson, D-Ill., announced her candidacy Monday, the Chicago Sun-Times reported.
Halvorson unsuccessfully challenged Jackson in the March 20 primary, picking up about 24 percent of the vote to 58 percent for Jackson. She represented the 11th Congressional District from 2009 to 2011 and was a state senator for 12 years prior to that. After redistricting, she wound up in Jackson's 2nd Congressional District.
Jackson resigned his seat Wednesday to deal with legal issues, including an investigation into whether he misused campaign funds.
Jackson, 47, had been on medical leave from Congress since June and has been receiving treatment at the Mayo Clinic in Minnesota. After he left the clinic for the second time recently, media reports indicated a federal investigation of alleged misuse of campaign funds to pay for personal items had included his wife, Chicago Alderman Sandi Jackson, who reportedly receives $2,000 a month as a political consultant.
Jackson was reported in plea negotiations with federal prosecutors. The Sun-Times said Jackson hired attorney Dan Webb, a former federal prosecutor.