"He is building an organization and telling family and friends that he is in fact going to be a candidate for the Senate from Illinois," the person told CNN in a story published Thursday.
A spokeswoman for Chris Kennedy, an Illinois businessman, acknowledged he is "seriously considering" a Senate bid.
"He has conducted polling which indicates a strong interest," spokeswoman Kasey Madden said. "But there is no time line for a decision or an announcement."
An Illinois Democrat told CNN Kennedy's allies are indicating to state Democratic officials Kennedy would seek the party's nomination for the seat once held by President Barack Obama and now occupied by Roland Burris.
Burris, a former state attorney general, was appointed to fill Obama's unexpired term by former Gov. Rod Blagojevich, who was impeached and indicted on federal charges alleging that he tried to profit from the vacancy in the U.S. Senate, among other things.
Chris Kennedy is the president of Merchandise Mart in Chicago.