Updated 01/25/13 – 11:38 a.m.

CHICAGO (CBS) – As discussions swirl about who will run for governor next year, one big question is: should Illinois Attorney General Lisa Madigan choose to challenge Gov. Pat Quinn, will her father, House Speaker Mike Madigan, step down to avoid a possible conflict of interest?

CBS 2 Chief Correspondent Jay Levine reports there have been both curious and cryptic responses from all involved.

A spokesman for Mike Madigan said the issue of whether the speaker would retire or step aside would be dealt with if and when Lisa Madigan decides whether to run for governor, while Lisa Madigan has refused to say anything at all on the subject.

“You have to deal with the House, if you’re governor, every single day, and I think it’s important that no members have conflicts of interest, and those who are in executive office shouldn’t have conflicts of interest,” Quinn said. “Especially as we clean up from my two predecessors, who are still in jail right now at the same time, we want to clean up government.”

Quinn has said he plans to run for re-election, and could face a challenge from Lisa Madigan, who has long been one of the most popular Democrats in the state.

Her father – as House Speaker – could determine the success or failure of Quinn’s legislative agenda in Springfield during the campaign.

Mike Madigan spokesman Steve Brown said there is no conflict of interest.

“That was effectively dealt with 10 years ago when voters overwhelmingly elected Lisa to Attorney General. She has worked well with the Speaker. There have been good outcomes on credit reporting and mortgage fraud,” Brown said. “Voters have put both Madigans in positions of power. With good outcomes.”

“There’s no conflict,” Brown added.

But the arm’s length relationship between the Madigans as House Speaker and Attorney General is different from the relationship between the speaker and the governor.

With the recent failures in the House to come up with comprehensive pension reform, some Springfield observers have suggested Speaker Madigan might be dragging his feet, and setting the stage for his daughter to ride in on a white horse and solve the state’s biggest problems.

“I work with the Speaker of the House, the President of Senate on all kinds of legislation. I presume that everything they do is for the people of Illinois, the common good,” Quinn said.

Bill Daley, another possible Quinn challenger, said Thursday that part of the reason he’s held off on running for governor in prior years was that his brother, Richard M. Daley, was mayor of Chicago at the time.

“But it wasn’t the only factor,” Daley said. “I assume it would be a factor for the Madigans as well.”

Lisa Madigan refused to admit that, or anything else, calling questions about a potential conflict of interest “premature.” According to her spokesperson, “the Attorney General is focused on her job.”

Potential Republican candidate for governor, Peoria Congressman Aaron Schock, couldn’t resist taking a shot when asked about the Madigans.

“Given the state of our state, why would we elect not only someone of the same party, continue to elect people of the same party, with the same policies and beliefs, now from the same family?” Schock said. “To me that’s crazy as a state. … Do you really expect different results?”

Schock on Thursday sounded less like a candidate for governor, and more like a man focused on his future in Congress.

But it was the cryptic response from Mike Madigan that could make this story big news, raising the possibility that if Lisa Madigan were to decide to run for governor, he’d have to decide whether to step down from the power post he’s held for nearly three decades.