Governor Eric Greitens of Missouri was recently indicted and arrested by local police.
https://www.nytimes.com/2018/02/22/us/eric-greitens-indicted.html
The Missouri Constitution says that the governor can be impeached and would be tried by a Senate-selected panel of judges. Like the US. Constitution, it does not say anywhere that the governor can be indicted, nonetheless, this doesn't seemed to have been a problem.
Of course, we are talking about federal law, which is different, but if there is no applicable federal precedent, federal courts often look to state courts for guidance if there are state-level precedents. The state precedents don't bind the federal courts, but if governors can be arrested based on similarly-worded state constitutions, then it's a good argument that the president can be indicted.
I am sure Mueller noticed this.
Missouri Constitution Article VII:
Section 1. Impeachment—officers liable—grounds.—All elective executive officials
of the state, and judges of the supreme court, courts of appeals and circuit courts
shall be liable to impeachment for crimes, misconduct, habitual drunkenness, willful
neglect of duty, corruption in office, incompetency, or any offense involving moral
turpitude or oppression in office.
Section 2. Power of impeachment—trial of impeachments.—The house of representatives
shall have the sole power of impeachment. All impeachments shall be tried
before the supreme court, except that the governor or a member of the supreme court
shall be tried by a special commission of seven eminent jurists to be elected by the
senate. The supreme court or special commission shall take an oath to try impartially
the person impeached, and no person shall be convicted without the concurrence of
five-sevenths of the court or special commission.