As you know ... Trump wants to settle the "hush" agreement battle with Stormy in arbitration. He and his attorney, Michael Cohen, say that's what Stormy agreed to do when she signed the deal.

But Stormy says not so fast. In docs filed Monday, she says "If Mr. Trump and Mr. Cohen are to be believed ... Mr. Trump never consented to the [hush agreement] because he never even knew about it."

She points out ... the President admitted not knowing about it on April 5 -- a reference to Trump's answer to reporters last week aboard Air Force One.

Stormy says there's nothing binding about that "hush" agreement -- and its arbitration clause -- if Trump didn't know about it, and as she said before ... never even signed it.