I don't think it is State, you heard it here 1st, I think his Dept would be Energy. I have heard it is a topic he is passionate about is energy aka that we don't have a cohesive energy policy. Comparing oil vs "X, Y, Z" alt energy sources in terms of cost effectiveness and a road-map for the future might be a fit for Mulally. That and the fact he is a rock star / turn around expert, makes him a win-win IMHO to be the fixer @ Energy.
I read a good analysis today that posited you need somebody skilled at reorganizing big enterprises, getting the company on a single mission, and knows how to “right-size” an organization. ExxonMobil has about 90k people — State is 1/3 of that. I think he would,be brilliant at State.