Spokeswoman Kasey Madden didn't say Wednesday when Chicago businessman Chris Kennedy would make an announcement.
The seat Kennedy is interested in is now held by Sen. Roland Burris, who was appointed by ousted former Illinois Gov. Rod Blagojevich.
Chris Kennedy's father was a U.S. senator when he was assassinated in 1968. He is a nephew of the late President John F. Kennedy and current U.S. Sen. Ted Kennedy of Massachusetts. His cousin, Caroline Kennedy, earlier this year dropped a bid to be appointed to a Senate seat from New York.