Yes, probably, particularly given the current composition of the U.S. Supreme Court. But this is a tricky question as it is both hypothetical, and it can be confused with questions about the advisability or legality of specific acts. The fact that someone has a right does not imply it insulates him from legal consequences, (e.g. I have a right to free speech, but yelling fire in a crowded theater can still subject me to legal consequences.)
The general rule, as expressed in Chevron U.S.A., Inc. v. NRDC, 467 U.S. 837 (1984), is:
A government agency must conform to any clear legislative statements when interpreting and applying a law, but courts will give the agency deference in ambiguous situations as long as its interpretation is reasonable.
This seems to be called the Chevron deference rule; that's a bit odd because they didn't defer to Chevron... Lawyers can argue isn't a hard and fast rule, and that seems to be true, but under the current (more conservative) court, it isn't likely to be ignored.
A key fact is that the DOJ is an Executive Department, and the Executive Branch of government has authority that is vested a strict hierarchy. The DOJ is distinct from independent agencies, like the Federal Election Commission, where the authority of the President is more restricted. There can be have been exceptions to the general rule for independent agencies, which are governed by board which the president can only remove for "good reason."
The president's authority over the executive departments flows from the first sentence in the U.S. Constitution, Article II section 1:
The executive Power shall be vested in a President of the United States of America. He shall hold his Office during the Term of four Years, and, together with the Vice-President chosen for the same Term, be elected, as follows: ...
This choice to create an separate executive branch with authority vested through a single individual (rather than a commission or committee) was explicit and well documented by the framers of the constitution.
Under the Judiciary Act of 1789, the statutory authority of U.S. Attorneys were independent of the Attorney General, and predate the Department of Justice but the subsequent 1870 act to establish the Department of Justice made clear that it was an executive department, establishing that the U.S. Attorneys became subordinates to the A.G. in that organization.
In a case that could reasonably be labeled "micromanagement", in 1893 Grover Cleveland dismissed a U.S. Attorney, without explanation, and without going through the Attorney General. It took till 1897 for the controversy to be resolved. The Supreme Court, in a surprisingly clear ruling said:
The President has power to remove a district attorney of the United States when such removal occurs within four years from the date of the attorney's appointment and, with the advice and consent of the Senate, to appoint a successor to him.
Parsons v. United States, 167 U.S. 324 (1897) with "four years being the period of appointment for U.S. Attorneys.
In a later case, involving a postmaster, the court said:
The President is empowered by the Constitution to remove any executive officer appointed by him by and with the advice and consent of the Senate, and this power is not subject in its exercise to the assent of the Senate, nor can it be made so by an act of Congress.
Myers v. United States, 272 U.S. 52 (1926) at 119.
None of this answer should be taken to mean that it is a good idea for a President to intervene in criminal prosecutions. IMHO, if it were done as an official action, it could be argued it was an abuse of power, but given this history arguing a president lacked the power seems imprecise. The important thing is that having an authority does provide a defense against a charge of abuse of authority or conflict of interest, but that wasn't the question asked.
P.S. For bipartisan thoughts about the complexity this situation, try this lawfareblog entry: Could Congress Simply Codify the DOJ Special Counsel Regulations? I won't quote as it doesn't directly answer the original question, but it may relieve you if you find my answer disturbing.