The Olympics Want Tiger Woods. He Wants to Go. But There’s a Catch.

“I know TV companies for obvious reasons are excited about it,” said Peter Dawson, the International Golf Federation’s president.

So, it would appear, is the host country. In October, roughly 60 miles from the Olympic venue, Japanese fans cheered louder for Woods than they did their native son, Hideki Matsuyama, at the inaugural Zozo Championship, which Woods won wire to wire.

Yes, Woods is currently the odd man out among Americans. But that is, as Dawson joked, “nothing that another Masters win wouldn’t cure.”

In 2016, the top four men in line to headline the Olympic field — Jason Day, Jordan Spieth, Rory McIlroy and Johnson — chose not to compete for reasons that included the fear of contracting the mosquito-borne Zika virus. This year, it’s possible an American player or two could be sidelined by something else: money.

The men’s competition in Tokyo will take place two weeks after the British Open and two weeks before the start of the three-tournament FedEx Cup playoffs, which offer a $60 million total purse, including a $15 million payoff to the eventual winner.

The first playoff event is outside Boston, 14 time zones from Tokyo, and so it is not unthinkable that a top player, prioritizing majors over medals or playoff riches over Olympic gold, might decide that it’s not worth making the round-the-world journey to Japan at such a key moment in his season.

Could somebody also stay home because of outside pressure to step aside to make room for Woods?

“There may be some of that,” Dawson said, though he quickly added, “I’m sure Tiger wouldn’t want to get into the Games that way.”