The relationship between Apollo and the White House runs deep. In 2017, Josh Harris, a founder of Apollo, advised the Trump administration on infrastructure policy and discussed a possible White House job with Jared Kushner, Mr. Trump’s son-in-law and senior adviser. That same year, Apollo lent $184 million to Mr. Kushner’s family real estate firm, Kushner Companies, to refinance the mortgage on a Chicago skyscraper.