With a lot of speculation and very s-l-o-w-l-y:

I spoke to one of my Thompson sources.
[…]
He has not spoken to any other campaign or any other candidates, nor does he intend to at this time.
He will not endorse, I am told by this source close to Thompson.
I am also told, “he has no interest in a vice presidency or a cabinet position.” At an “appropriate time” he will outline his plans for the near future.
[…]
At one point, I asked this source if the attitude was, ‘if you can’t be Reagan, be Goldwater,’ and the source responded, “exactly.”