Jackson is under investigation for allegedly using campaign funds to decorate his Washington home, as well as to buy a $40,000 Rolex watch as a gift for a female friend, the newspaper said.
WLS-TV, Chicago, reported the discussions have been ongoing for a while.
"No one has pled guilty, but plea discussions are ongoing," an unnamed source told the newspaper, adding Jackson is still undergoing treatment at the Mayo Clinic for depression and bipolar disorder.
Jackson also is under investigation by the House ethics panel. The investigations began as the case against former Illinois Gov. Rod Blagojevich became public. Blagojevich, who is serving a 14-year federal prison sentence, tried to sell the U.S. Senate seat vacated by Barack Obama in 2008. Jackson was among those vying for appointment to the seat.
Jackson was elected to a 10th term in the House Tuesday, despite having not campaigned. He has been on medical leave from the House since June.
"I am humbled and moved by the support shown today," Jackson said in a statement. "Every day, I think about your needs and concerns. Once the doctors approve my return to work, I will continue to be the progressive fighter you have known for years."