(CNN) Jeff Sessions loves his job as US attorney general, but powerful Republicans keep floating his name as the party's favorite write-in candidate for the Alabama Senate race.

Meanwhile, President Donald Trump never misses a chance to bemoan how " disappointed " he is with the Justice Department.

Neither Trump nor the attorney general have publicly responded to the chatter that Sessions might return to his old Senate seat. But sources tell CNN that Sessions has said he's not interested.

But in the event Sessions ultimately resigns or Trump escalates his frustrations and fires him, here's what could happen next:

1. Who is immediately in charge?

If Sessions goes, then Deputy Attorney General Rod Rosenstein, the current No. 2 at the Justice Department, would automatically take his place -- at least, according to statute and the President's own executive order detailing the succession plan from March.

If, for whatever reason, Sessions and Rosenstein are both fired (or quit), Associate Attorney General Rachel Brand would elevate to acting attorney general.

And moving even further down the line -- if Sessions, Rosenstein and Brand are all gone, then Noel Francisco, the solicitor general, would be the next person tapped to serve as attorney general.

2. Can Trump pick someone else entirely?

Yes -- the President doesn't have to follow the usual course, but this is where things could get tricky.

Under the Federal Vacancies Reform Act , Trump can pick anyone who holds a Senate-confirmed position to serve as acting attorney general (subject to certain time limitations) -- but the person he selects as acting attorney general cannot then be named as the permanent successor.

By its terms, the act applies whenever a Senate-confirmed officer in an executive agency dies, resigns or is "is otherwise unable to perform the functions and duties of the office." But it's arguably an open question as to what happens if the officeholder is instead fired by the President.

3. What about a recess appointment?

Another option is for Trump to announce a replacement for Sessions during the next Senate recess -- a so-called "recess appointment" who could then serve until the end of the next Congress.

But this past summer, when the President unleashed a daily barrage of morning tweets slamming Sessions, Senate Democrats indicated they would almost certainly try to block such an appointment.

"All Americans should be wondering: Why is the President publicly, publicly demeaning and humiliating such a close friend and supporter, a member of his own Cabinet?" Senate Minority Leader Chuck Schumer said in July. "They should wonder if the President is trying to pry open the office of attorney general to appoint someone ... who will fire Special Counsel (Robert) Mueller and shut down the Russia investigation."

"Let me say, if such a situation arises, Democrats would use every tool in our toolbox to stymie such a recess appointment," he added.

While Republicans control the Senate, the only way they can formally adjourn (which would set up a period when recess appointments are available) is to pass an adjournment resolution. However, Democrats can filibuster that resolution, which they would do to prevent Trump from making a recess appointment.

4. What happens to Mueller's investigation if Sessions is out?

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Speaking of Mueller, his Russia probe is currently under the supervision of Rosenstein (because Sessions recused himself from all things related to the presidential campaigns).

Indeed, the recusal fallout is the primary stated reason Trump has continuously unleashed a fury on his attorney general.

For the time being, only Rosenstein currently has the power to remove Mueller for "misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of (Justice) Departmental policies" under the special counsel regulations.

But if Sessions is fired, and his replacement doesn't have the same conflict overseeing the investigation, then Rosenstein would no longer be in charge, and Trump's new attorney general could potentially fire Mueller.

An earlier version of this story was published in July.