That contradicted Trump's statement last month in a Fox News interview, during which the President said: "I know Matt Whitaker."
Conway said today that Trump was trying to make the point on Saturday that in selecting Whitaker for the acting attorney-general job, he wasn't appointing "a friend there who he's known his entire life".
She added that it wasn't clear whether Whitaker had been briefed on the Mueller probe.
"He's been the chief of staff to a recused attorney-general," she said.
Trump had been aware before appointing him that Whitaker was a sceptic of the Mueller probe, which factored into the decision to tap him over Deputy Attorney-General Rod Rosenstein, two White House advisers told the Washington Post.
Speaking on ABC News' This Week, Conway said the President chose Whitaker because he wanted to "have a continuum" when it comes to people serving in the attorney -general role. She added that the Trump Administration had been "compliant" with the investigation and that she "can't really blame" the President "if he doesn't" meet Mueller.
Trump's legal team in August rejected Mueller's conditions for a sit-down interview, although Trump said at the weekend that he has not ruled out an interview with the Special Counsel.
Asked about the op-ed co-written by her husband, lawyer George Conway, in which he argued that Whitaker's appointment was unconstitutional, she said: "Spouses disagree".
In an appearance on CBS News' Face the Nation, Senator Lindsey Graham, (R), also defended Trump's appointment of Whitaker, describing the acting attorney-general as "legally qualified and otherwise qualified to oversee this investigation".
"I'm confident that Mr Mueller will be allowed to do his job without interference," Graham said, adding: "You don't recuse somebody because they have opinions different than the people they're overseeing."
