Trump team discrediting Mueller is probably one of their top priorities these days.
It must be worrying Trump quite a bit to be exploring his pardoning powers. The Washington Post has a good read on it.
Trump team seeks to control, block Mueller’s Russia investigation
The power to pardon is granted to the president in Article II, Section 2, of the Constitution, which gives the commander in chief the power to "grant Reprieves and Pardons for Offences against the United States, except in Cases of Impeachment." That means pardon authority extends to federal criminal prosecution but not to state level or impeachment inquiries.
No president has sought to pardon himself, so no courts have reviewed it. Although Kalt says the weight of the law argues against a president pardoning himself,
he says the question is open and predicts such an action would move through the courts all the way to the Supreme Court.
Some note that the Constitution does not explicitly prohibit a president from pardoning himself.
On the other side, experts say that by definition a pardon is something you can only give to someone else. There is also a common-law canon that prohibits individuals from serving as a judge in their own case. "For example, we would not allow a judge to preside over his or her own trial," Kalt said.
A president can pardon an individual at any point, including before the person is charged with a crime, and the scope of a presidential pardon can be very broad. President Gerald Ford pardoned former president Richard M. Nixon preemptively for offenses he "committed or may have committed" while in office.
https://www.washingtonpost.com/politics/trumps-lawyers-seek-to-undercut-muellers-russia-investigation/2017/07/20/232ebf2c-6d71-11e7-b9e2-2056e768a7e5_story.html?hpid=hp_hp-top-table-main_trumplegal-925pm%3Ahomepage%2Fstory&utm_term=.1f22cd24dac1
