The lawsuit asks the court to block the Fraternal Order of Police from paying for Burge's legal defense.
Burge is accused of lying under oath about torturing African-American suspects.
The lawsuit was filed by one current and one former Chicago police officer. They argue the union refused to pay their legal fees while funding Burge's defense.
"According to the city, when they paid for his legal defense, it was upwards of five, five-and-a-half, to six million dollars. And if that's any type of indicator, he will, Jon Burge will bankrupt our fund by himself," said Officer Joe Shaw, spokesman for the officers.
A hearing scheduled Thursday on the lawsuit was postponed until Friday morning.
