From Serolf Divad at Stinque:
As usual Donald Trump is trying to be too cute by half here, at once asserting that he is innocent of any real crime (it’s all just “fake news”) but at the same time insisting that “everyone” agrees that his pardon authority is unlimited and thus, one must surmise, applicable to himself.
Despite what Trump would like to believe there are real questions as to whether the president in fact has the power to pardon himself: see here and here. Now I’m no constitutional scholar, and not even a lawyer, but if I might offer an opinion I would suggest that the President’s inability to pardon himself follows from Article II, Section 2 of the Constitution where the power of the pardon is explicitly granted to the President and its limitations laid out:
The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States; he may require the Opinion, in writing, of the principal Officer in each of the executive Departments, upon any Subject relating to the Duties of their respective Offices, and he shall have Power to grant Reprieves and Pardons for Offenses against the United States, except in Cases of Impeachment.
What is of interest here is the bit I have reproduced in bold.