1. Petraeus is a convicted criminal.
2. Corker has been an Obama flack in the Senate for years.
3. I don't think a military guy is well suited for this role, especially when the top goal of the Trump administration should be changing gears on the military interventionism that has dominated U.S. foreign policy for 25 years.
P.S. — I would not be shocked if Trump’s nominee for Secretary of State is someone who hasn’t even been mentioned in these media stories.
The Generals are usually much less eager for military interventions (and especially nation building) that the politicians.