President Trump says he doesn't want Special Counsel Robert Mueller to testify before Congress, and on Wednesday he asserted executive privilege over the entirety of Mueller's report. But that doesn't necessarily mean he can stop Mueller from speaking.

The Democrat-run House Judiciary Committee formally invited Mueller to testify last month, although no date has been officially set. Mr. Trump's stated in a Sunday tweet that "Bob Mueller should not testify," a position White House officials have subsequently backed up.

"Is Mueller going to go to Capitol Hill and say, oh you know what I forgot - milk, butter, eggs, indictment, crime? He's not going to say that. There is no criminal referral," top Trump adviser Kellyanne Conway told reporters outside the White House Tuesday.

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Mr. Trump had previously said that he would defer to Attorney General William Barr on whether Mueller should testify. But the president's latest position is more in line with his administration's general stance on top officials testifying and turning over documents, with Mr. Trump saying they're fighting "all the subpoenas."

Still, it's unclear how the administration might attempt to stop Mueller from testifying, what it can do if it decides to try. The House Judiciary Committee's negotiations with Mueller about the possibility of him testifying are still ongoing, House Judiciary Chairman Jerry Nadler told reporters Wednesday afternoon. Nadler said the president's tweet puts a lot of "pressure" on the president not to testify.

Stopping Mueller's testimony altogether

Could the Trump administration stop Mueller from testifying before Congress entirely, either in public or in a closed-session hearing, if Mueller agrees to appear? That is highly unlikely, according to legal experts, particularly since the special counsel's office is winding down.

Andrew Napolitano, a former judge and top Fox News judicial analyst, said there is nothing the White House can do if Mueller quits and decides to testify.

"Bob Mueller can negate all of this by resigning from the [Department of Justice], saying my job is over," Napolitano said on Fox Business Monday. "Then he's a private citizen and nobody can stop him."

Napolitano suggested the president can stop a government employee from testifying, but not a private citizen.

"The report is 99 percent public," Napolitano said. "The author of the report has helped make it public. He certainly lawfully can testify about it."

Even with Mueller being a current Justice Department employee, it's not completely clear whether the president or attorney general could keep him from testifying, said Frank Bowman III, a law professor at the University of Missouri who has authored a book on a related topic due out later this year, "High Crimes & Misdemeanors: A History of Impeachment for the Age of Trump."

But the question becomes much clearer when Mueller is inevitably a private citizen.

"On what ground would they do so?" Bowman said of the possibility of the administration stopping Mueller from testifying.

"I can't even conceive on what ground any serious lawyer would even file such a suit," Bowman said.

Chris Traux, a legal adviser with Republicans for the Rule of Law, a nonprofit group of longtime Republicans that fought to make the Mueller report public, also doesn't see a way for the Trump administration to stop Mueller from testifying.

"There is no way to compel legally compel a witness to not speak — especially one who is no longer like an employee," Traux said.

The executive privilege option

The matter becomes more complicated when it's question of whether the president can stop Mueller from testifying about certain topics.

"I think there's a distinction between having him come and testify and whether or not there may be questions he can or cannot answer," Traux said, adding, "That's where it starts to get tricky."

In theory, the White House could invoke executive privilege, which allows the administration to resist revealing some information to the other branches of government, in trying to prevent Mueller from testifying about what it deems to be sensitive matters.

"If the claim being made is that Mueller can't testify because the president is exerting executive privilege…that's the president's call to make," Bowman said.

But claiming executive privilege over Mueller's testimony isn't as straightforward as it would be for other executive branch officials. For example, executive privilege claims are often strongest when they involve direct conversations with the president and his advisers.

But the Trump administration could still try to invoke privilege about interagency communications, said Jonathan Turley, a George Washington University Law professor and CBS News legal analyst.

"The Mueller report is a 400-page waiver of executive privilege," Turley said. "However, the White House can argue that communications with Mueller is like the executive branch speaking with itself. Under this theory, any documents or evidence not disclosed in the actual report could still be claimed as privileged."

The White House could argue that if Mueller wants to say anything not explicitly in the report, that would "likely stray into privileged areas," Turley suggested.

"Thus, if Mueller is asked about evidence not contained in the report, it would trigger a privilege fight," Turley said.

On Wednesday, the president claimed executive privilege over the entire Mueller report and any underlying documents. But Bowman doesn't think that necessarily changes the situation related to Mueller testifying.

"I don't think it changes the legal posture at all," Bowman said. "I don't think the White House thinks so either. But it would delay things because there will be all sorts of preliminary discussion and negotiation internally within DOJ, and between DOJ and White House. And between executive branch and judiciary."

If all that doesn't compel Mueller's testimony, a subpoena will be issued, triggering "rounds of discussion," Bowman said.

"If he decides to comply, either before or after resigning from DoJ, then anticipate a White House effort to stop him through a (frivolous) court action," Bowman wrote.

Bowman, however, insisted the executive privilege claim would be a hard one back up.

"The claim of executive privilege can really only be extended to advice that's given to the president or perhaps communications that could be said to undergird advice given to the president," Bowman noted.

"It's hard to imagine that any serious claim on that basis could prevent Mueller from testifying."