But this guidance may conflict with the Code of Federal Regulations, which says "the Special Counsel may be disciplined or removed from office only by the personal action of the Attorney General."
Senate minority leader Chuck Schumer, D-N.Y., referred to the federal rule in his response to Sanders' comments at the briefing.
The Justice Department regulations "could not be more clear; the president does not have the authority to remove Special Counsel Mueller," a spokesman for Schumer said.
Sanders' comments indicated that White House staff, and possibly the president, have sought advice on whether Trump could order the special counsel terminated.
Sanders didn't immediately respond to an email asking whether there have been discussions in the White House about firing Mueller and whether Trump has actively sought advice about it.
Reporters also asked Sanders about the president's recent remarks on Attorney General Jeff Sessions, who has long been a target of Trump's ire over his recusal . The power Sessions abdicated fell to Deputy Attorney General Rod Rosenstein, whom Trump has reportedly also considered firing.
At the Monday evening briefing, Trump offered some of his harshest criticism yet for the head of his own Justice Department. "The attorney general made a terrible mistake when he did this," Trump said of Sessions' recusal. Had Sessions let Trump know he was planning to recuse himself over failing to report contacts with a Russian ambassador in congressional testimony, "we would have used a — put a different attorney general in," Trump said.
Sanders affirmed that Trump's words represented his feelings about Sessions, saying "the president was pretty clear about his frustrations when he spoke about that last night."
Asked if John Bolton, who began his tenure as Trump's new national security advisor on Monday, forced homeland security advisor Tom Bossert to resign, Sanders said she is "not going to get into specific details about ongoing personnel." She added, however, that Trump feels Bossert has "done a great job."