Jared Kushner, President Donald Trump’s son-in-law and close adviser, met with a senior Time Warner Inc. executive in recent weeks and expressed the administration’s deep concerns about CNN’s news coverage, according to a White House official and other people familiar with the matter.

In a meeting at the White House, Mr. Kushner complained to Gary Ginsberg, executive vice president of corporate marketing and communications at CNN’s parent Time Warner, about what Mr. Kushner feels is unfair coverage slanted against the president,...