No.
And he will probably be happier spending more time on his ranch.
Tillerson was CEO of a huge corporation. I suspect he has the Texas disease, direct speak. No sugar coating. (Trumps NY bluntness, and Tillerson’s direct speak clash)
Both Tillerson and Trump are very opinionated.
Their both bosses! You can’t have someone on your team who thinks they would do a better job sitting in your chair!