Preckwinkle defeated Stroger last year in the democratic primary when he ran for a second term. He finished last in a four candidate race.
Stroger was paid $170,000 a year as the county's chief executive. He filed for jobless benefits in January but the county's human resources bureau opposed his application.
"I don't think it's appropriate for elected officials who lose elections to apply for unemployment compensation. My understanding from staff is that he's ineligible," Preckwinkle said.
Preckwinkle stressed that the final decision on whether Stroger receives unemployment compensation is made by a state agency not by her.