Mr. Woods has appeared happy to return the support. The day before the 2014 World Golf Championships-Cadillac Championship, Mr. Woods appeared with Mr. Trump and three of his children to inaugurate the Tiger Woods Villa at Doral.

“What Donald has done with this place is phenomenal, and he does nothing halfway,” Mr. Woods said at the ribbon-cutting. One month later, Mr. Woods announced the Tiger Woods Charity Playoffs, a series of nine charity golf tournaments for amateurs. One of the eight regional qualifiers was held at the Trump National Golf Club in Bedminster, N.J.

That year, Mr. Trump also announced that Mr. Woods would design a course for his Dubai property. While Mr. Woods’s team has tried to play down the business connection, arguing that the golfer’s contract was with the developer, DAMAC Properties, Mr. Trump has been eager to advertise Mr. Woods as his business partner. On Twitter, he has shared links that mention that the two men are “teaming up” and that Mr. Woods is “working for” Mr. Trump.

The course, which was expected to be completed by the end of 2017, has yet to open, however. Glenn Greenspan, the longtime spokesman for Mr. Woods, did not respond to a request to discuss their business ties.

Nonetheless, Mr. Trump has made it known over the years that he sees Mr. Woods as a great investment. “I want to sponsor those children,” he told Extra TV in 2013, when he was asked to weigh in on the romantic relationship between Mr. Woods and Lindsey Vonn, the champion World Cup ski racer. The two are no longer a couple.

And when Mr. Woods won a tournament at the Trump National Doral by two strokes that year, Mr. Trump used the moment to plug his course as one of the greatest in the world, promoting the victory — and himself — on Twitter and in an interview on “Fox & Friends.”

Mr. Woods has played golf with Mr. Trump at least three times since the pairing became a political statement: twice since Mr. Trump became president and once when he was the president-elect. Mr. Woods, who has taken some blowback for engaging with Mr. Trump, has argued that he is not a political person and simply respects the office of the president.