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(CNN) —  

Special counsel Robert Mueller could testify before the House Judiciary Committee as early as next week, in what could become the most consequential congressional hearing of the Trump administration.

But it’s not as simple as Mueller simply showing up to the committee room.

While Attorney General William Barr said last week that he has no objections to Mueller appearing before Congress, President Donald Trump reversed course and tweeted Sunday that Mueller should not testify.

Still, a hearing with Mueller remains on track to happen – and soon. Here’s what you should know about his potential upcoming testimony on Capitol Hill.

When is the hearing?

The House Judiciary Committee has floated May 15 as the date for a public hearing with Mueller, though the committee has not yet finalized the date.

But that might not be the only time the special counsel heads up to Capitol Hill to talk about his report and 22-month investigation. The House Intelligence Committee has requested that Mueller brief the panel on the counterintelligence investigation into Trump and Russia behind closed doors, though that has not been confirmed yet either.

It’s also possible that Mueller could testify in the Senate. But it’s not likely to be in the Senate Judiciary Committee. Chairman Lindsey Graham, a South Carolina Republican, said he had no interest in bringing in Mueller after he held a hearing on the report with Barr last week.

“For me, it’s over,” Graham said of the Mueller investigation.

Graham did add one possible exception, sending Mueller a letter last week and asking if he wanted to add any testimony specifically related to how Barr described their telephone call about Mueller’s letter objecting to Barr’s characterization the investigation.

Graham told CNN Monday that he’s open to having public testimony from Mueller – or any other form that Mueller wants to provide it – about the Barr phone call. But Graham said that public testimony would just be about “any dispute” about the call.

Is Mueller allowed to testify?

Yes.

While Mueller has submitted his report, he still remains an employee of the Justice Department as the special counsel. And he’s still driving in to his nondescript Washington office every day.

Congress has formally requested his testimony, and so long as the Justice Department doesn’t object, Mueller can testify voluntarily. Barr was asked last week at a Senate hearing whether he had any issues with Mueller testifying, and Barr said he had no objections.

The format of the hearing has not yet been finalized either. It’s possible that Mueller won’t be the only one appearing from his team, and it’s not clear whether he would be questioned just by lawmakers or also by staff attorneys – as House Judiciary Chairman Jerry Nadler tried unsuccessfully to do with Barr last week.

What are the sticking points?

A potential wrench was thrown into Mueller’s testimony on Sunday by Trump, who has claimed “total exoneration” from the Mueller report. The President had previously said he did not have a problem with Mueller testifying. But then he tweeted Sunday that Mueller should not testify.

“Bob Mueller should not testify. No redos for the Dems!” Trump tweeted.

An administration official familiar with the matter told CNN Monday night that Trump wasn’t necessarily signaling his intent to block Mueller from testifying with that tweet.

“The President was expressing his opinion that the investigation is over and it’s time to move on,” the official said.

Trump himself could not stop Mueller from testifying, but he could try to convince his attorney general not to allow his testimony. If the Justice Department were to change course and oppose Mueller appearing before Congress, lawmakers would have several possible options to try to bring him in anyway.

The first would be to wait until Mueller is a private citizen, although the special counsel’s office has given no indication when Mueller will leave the department.

The second would be to subpoena for his testimony.

In addition, the White House has another tool to try to limit Mueller’s testimony: claim executive privilege over certain elements of the report. The White House waived executive privilege for the special counsel investigation and didn’t try to block anything in the release of the report – but the White House argues it has not waived executive privilege for Congress, and still reserves the right to invoke it with the legislative branch.

What is he expected to say?