Tolkien writes in letter 192 that Eru directly intervened in the destruction of the ring (see the answer here).
Was Sauron aware that Eru was there ready to step in and give a cheeky push to Gollum? Would that explain his all consuming fear?
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This simply isn't something Tolkien deals with in any of his writings. It's certainly possible he detected it, but there's no confirmation one way or the other.
Tolkien writes in the essay "Notes on Motives" that Sauron almost certainly believed Eru had abandoned the world:
He probably deluded himself with the notion that the Valar (including Melkor) having failed, Eru had simply abandoned Ea, or at any rate Arda, and would not concern himself with it any more. It would appear that he interpreted the 'change of the world' at the Downfall of Numenor, when Aman was removed from the physical world, in this sense: Valar (and Elves) were removed from effective control, and Men under God's curse and wrath.
History of Middle-earth X Morgoth's Ring Part 5: "Myths Transformed" Chapter VII "Notes on motives in the Silmarillion"
There's no reason to believe that Sauron would have expected Eru to intervene at this point.