The 83-year-old was sentenced to seven and half years behind bars for bribery conspiracy and other corruption counts.
He is scheduled to report to prison on Oct. 13.
In a new filing, Madigan's lawyers argue the jury was mis-instructed on key legal standards.
The court has not ruled on that request yet.
A federal judge previously denied Madigan's request to stay out of prison, while his appeals play out.
The ex-speaker recently hired a team of attorneys who have years of experience arguing at the U.S. Supreme Court.
Capitol News Illinois contributed to this report.