And those on the Ed Sec watch read their tea-leaves.

Arne Duncan, the schools chief in Chicago and President-elect Obama’s informal adviser and basketball buddy, has frequently been mentioned a possible pick for Secretary of Education. He and Secretary Spellings apparently had coffee this morning.

So was Secretary Spellings giving him advice?

No, Duncan told the Associated Press. Apparently it was just a social call. They worked together to plan an event in Chicago next week.

My guess is that the meeting between Duncan and Spellings may seem like more than what it was. If Duncan was meeting with Obama, his incoming chief of staff Rahm Emanuel, or transition team honcho John Podesta, it would be more indicative that he’s about to take on a cabinet position.

The AP story also mentions a couple of education secretary possibilities I hadn’t heard yet, including Virginia Gov. Tim Kaine and former Georgia Gov. Roy Barnes, who was a co-chairman of the Aspen Institute’s Commission on the Future of No Child Left Behind.

My guess? Not Barnes. The Aspen report’s emphasis on upping the ante on accountability, including voluntary national standards and data systems to measure teacher effectiveness probably tilts him too far in one direction in a Democratic party divided over how to proceed on the NCLB law.

Kaine is an intriguing possibility. Right now, he is the chair of the Southern Regional Education Board. As governor of Virginia, he has worked to expand pre-kindergarten classes, bring teacher salaries up to the national average and raise the quality of the state’s career and technical programs, according to SREB. And I’ve heard he’s really passionate about education and gets the issues. He was an early Obama supporter—and rumored vice presidential pick. But it’s hard to say if he’s seriously in contention—or if some folks out there just wish he was.

UPDATE: Looks like Kaine isn’t interested in the job after all.