President Trump on Friday discussed making Sidney Powell, who as a lawyer for his campaign team unleashed a series of conspiracy theories about a Venezuelan plot to rig voting machines in the United States, a special counsel investigating voter fraud, according to two people briefed on the discussion.

It was unclear if Mr. Trump will move ahead with such a plan.

Most of his advisers opposed the idea, two of the people briefed on the discussion said, including Rudolph W. Giuliani, the president’s personal lawyer, who in recent days sought to have the Department of Homeland Security join the campaign’s efforts to overturn Mr. Trump’s loss in the election.

Mr. Giuliani joined the discussion by phone, while Ms. Powell was at the White House for a meeting that became raucous at times, according to one of the people briefed on what took place. Other administration officials drifted in and out of the meeting, two of the people briefed said, and the White House counsel, Pat A. Cipollone, pushed back on the ideas being proposed.