TOKYO — If anyone can stir Japanese national pride at the moment, it is Naomi Osaka.

The world’s No. 1-ranked player in women’s tennis, Ms. Osaka is among the biggest stars in Japan, splashed across television programs and advertisements for Nissan cars and Citizen watches. As a mixed-race person, she has also helped prompt a discussion about how Japanese see their country.

But a looming deadline — Ms. Osaka’s 22nd birthday in October — has raised the question of whether she can continue to represent Japan on the international tennis circuit, where she has given the country bragging rights on the world sports stage.

Ms. Osaka, whose mother is Japanese and father is Haitian-American, has citizenship in both Japan and the United States. Under Japanese law, dual citizens must choose between the two nationalities by the time they turn 22.

That legal clause has left fans and commentators trying to guess whether Ms. Osaka will pick citizenship in Japan, the country of her birth, or the United States, where she has lived since she was a young child.