Trump just announced on Twitter that Tillerson is not leaving as his Secretary of State, despite their disagreements:
The media has been speculating that I fired Rex Tillerson or that he would be leaving soon - FAKE NEWS! He’s not leaving and while we disagree on certain subjects, (I call the final shots) we work well together and America is highly respected again!https://t.co/FrqiPLFJ1E— Donald J. Trump (@realDonaldTrump) December 1, 2017
My guess is that Tillerson probably asked Trump to reiterate this to dispel of the rumors flying around the media about his looming departure.
Either way, Trump has put a nail in this one for now.