Former Chicago mayor Jane Byrne wants to return to public office. But since her loss in the Democratic primary to Mayor Harold Washington, she has set her sights a little lower. Byrne said last week that she is "leaning toward" running for Cook County Circuit Court clerk.

Washington, who once said Byrne's Chicago was a "city run by bandits," said he'd be "more than happy" to help Byrne. Short of endorsing her, he said she would be a "decided improvement" over current clerk Morgan Finley, who was indicted recently on charges of conspiracy, extortion, fraud and racketeering.

Meanwhile Edward R. Vrdolyak, chairman of the Cook County Democratic Party and Washington's most vocal opponent in the city council during the mayor's first term, is considering becoming a Republican, according to Illinois GOP leaders.

Vrdolyak, out of office after challenging Washington this year as a third-party candidate, would like to run for state's attorney, the job held by Richard M. Daley. But that's being discouraged, GOP leaders say, because of Vrdolyak's less than pristine reputation as a wheeler-dealer. He is now eyeing a race for county clerk -- the same job Byrne is looking at.

Some GOP stalwarts, such as Cook County Republican chairman Don Totten, are less than thrilled with the prospect of having Vrdolyak in their midst. "You put together the chairman of the Democratic Party with the Republican Party and you've got something," said Totten. "I'm just not sure what."