As President Trump greeted dignitaries and business leaders on Tuesday during his state visit to Saudi Arabia, he was met by a very familiar face: Gianni Infantino, the president of soccer’s governing body, FIFA, who has been a loyal backer since Mr. Trump’s first term. The close relationship between Mr. Trump and Mr. Infantino, a Swiss-Italian soccer administrator, has for years raised eyebrows in soccer circles and beyond. The friendship appears to go beyond one between a leader of a World Cup host nation — the United States is co-hosting the next edition of the quadrennial tournament in 2026 with Mexico and Canada — and the head of global soccer. On Wednesday, Mr. Infantino will join Mr. Trump on the second leg of his presidential tour of Gulf States in Qatar, the thumb-shaped peninsula bordering Saudi Arabia that hosted the World Cup in 2022. The soccer boss is expected to preside over a ceremony in which the emir of Qatar, Sheikh Tamim bin Hamad al-Thani, will hand World Cup hosting duties to Mr. Trump. Representatives of Canada and Mexico are not expected to be present. At the White House last week, Mr. Trump, whose tariffs have stoked tensions with the two U.S. neighbors, joked that Mr. Infantino had correctly downplayed their roles in the World Cup.