WASHINGTON—President Trump said this week that he never had any plans to fire Federal Reserve Chair Jerome Powell, accusing the media of pushing a false narrative that he was out to get the central bank chief.

But inside the White House, some senior officials took Trump’s recent public musings about terminating Powell seriously. As Trump’s criticism of the Fed chair ramped up over the last week, White House lawyers privately reviewed legal options for attempting to remove Powell, including whether they could do so for “cause,” according to people familiar with the matter. The laws that created the Federal Reserve say Fed governors can only be removed before their term ends for cause, which courts have generally interpreted to mean malfeasance or impropriety. Finding a pretext for dismissing Powell would have edged the White House closer to a dramatic confrontation with the central bank.