The tabloid is the city's second major newspaper, 13th largest in the United States, and is being sold by its parent Hollinger International after Chief Executive Officer Conrad Black resigned amid allegations he took millions in unauthorized payments.
Black's deal to sell the newspaper to Britain's Barclay brothers fell through.
Crain's Chicago Business said Yusef Jackson, a lawyer who heads a lucrative Anheuser-Busch distributorship, bid for the paper with supermarket magnate Ronald Burke.
Jackson, 33, reportedly is only interested in the Sun-Times and not Pioneer Press, Star Newspapers or dozens of other Hollinger-owner publications in the Chicago area.
His father, Jesse Jackson Sr., writes a weekly column for the Sun-Times.
Crain's said the deadline for final bids is March 23.