Russia attempted to resolve the "Ukraine issue" in a swap arrangement with the U.S. involving influence over Venezuela, that's according to Deputy Assistant to the President and Senior Director for Europe and Russia on the National Security Council staff Fiona Hill, who testified as part of the Donald Trump impeachment inquiry.

As protests in Venezuela unfolded, the Russians were "signaling very strongly that they wanted to somehow make some very strange swap arrangement between Venezuela and Ukraine", Hill said in her testimony.

In other words, if the U.S. wanted to keep Russia out of its "backyard" [this is after the Russians had sent in a hundred operatives to secure the Venezuelan Government and to preempt what they thought could turn into a U.S. military action], Russians had their "own version" of this: "You're in our backyard in Ukraine."

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That message, Fiona Hill said, was being "sent to us, you know, kind of informally through channels."

She added that the Russian press and various commentators in Russia picked up on the narrative.

"And I was asked to go out to Russia in this timeframe to basically tell the Russians to knock this off. I was given a special assignment by the National Security Council with the agreement with the State Department to get the Russians to back off," Hill testified.

Hill testified before the House on October 14. The text of her testimony was released November 8.

On October 31, the House of Representatives voted to move the Donald Trump impeachment inquiry into a public plane.