Numerous names have been floated to replace Sessions, but there is no clear frontrunner, the people said. Among the possible candidates Trump and White House advisers have discussed are Representative John Ratcliffe of Texas, former New Jersey Governor Chris Christie, and Health and Human Services Secretary Alex Azar. There have also been a number of senators, former congressmen, and federal judges whose names are in the mix.

People close to the the process were hesitant to make any predictions about when the president would make a nomination.

Any nominee is likely to face intense questioning during confirmation hearings on how he or she would handle the Mueller investigation and demands for a commitment not to interfere in the probe or curtail it.