President Donald Trump didn’t mince words last fall when he explained to Dallas Cowboys owner Jerry Jones that he wouldn’t relent in his criticism of NFL players who were kneeling during the national anthem to protest social injustice.

“This is a very winning, strong issue for me,” Mr. Trump said in a phone call, according to a sworn deposition given by Mr. Jones and reviewed by The Wall Street Journal. “Tell everybody, you can’t win this one. This one lifts me.”

Mr....