“I feel like I’m in good shape from that standpoint—I probably won’t,” Mr. Trump said in an interview with The Wall Street Journal. “I’ll look at stuff later on. I’m not against it, but it’s probably not for me.”

The Food and Drug Administration has already authorized the additional shot for certain people with weakened immune systems. The agency had been expected to greenlight an extra dose for all three Covid-19 shots administered in the U.S. starting in mid-September. The timetable may be pushed back as regulators need more time to review the data, at least for the Moderna Inc. and Johnson & Johnson shots.

The initial booster campaign, federal health officials have said, may include recommending shots for people over 65 because they are seen as more vulnerable than younger people. Mr. Trump is 75.