WASHINGTON — President Trump has broadened his search for a new F.B.I. director in recent days, moving to install a leader who would be viewed as independent from the White House amid the backlash over his abrupt dismissal of James B. Comey.

Four candidates will be interviewed Saturday, according to a person familiar with the meetings: Andrew G. McCabe, the acting director of the F.B.I.; Senator John Cornyn, Republican of Texas; Judge Michael J. Garcia of the New York State Court of Appeals and the former United States attorney for the Southern District of New York; and Alice Fisher, a former top Justice Department official who would be the first woman to run the agency.

The timing of a nomination is far from clear; the White House press secretary, Sean Spicer, provided no firm timeline on Friday.

The candidate list is also said to be broader than those four. Mr. Trump has a long history of tossing names out as chum for public consumption, in part to throw people off the scent of what he is doing, and in part to test various options.