US Open champion Naomi Osaka Monday set her sights on Olympic glory in 2020 as she became only the second Japanese woman to reach number four in the world rankings.

The fast-rising tennis star, who turns 21 on Sunday, has already become Japan’s first Grand Slam singles champion after she stunned Serena Williams in New York last month.

And on Monday, she rose to a career-high ranking of four to become the top ranked Japanese woman since Kimiko Date in 1995.

Now she is targeting a strong performance at the WTA Finals Singapore later this month and she could yet finish her standout season as the top placed Japanese woman of all time.

Looking further ahead the Osaka-born dual US-Japanese national, who represents the country of her birth in tennis, has her eyes on the Tokyo Olympics.

“Everyone is really excited in Japan for the Olympics,” she told reporters at the WTA Hong Kong Open, which she has been forced to withdraw from with a back injury.

“I know that everyone — all the Japanese players — wants to do well and of course I share that same feeling.”

She added: “I really want to experience the moment and at the same time I know I want to win the gold medal — everyone who plays in the Olympics wants to win gold — so that would be my aim, but (also) overall just to have fun.”

Osaka, who has referred to her breakthrough victory at Flushing Meadows as “bittersweet” after it was overshadowed by an explosive row between Williams and the chair umpire, has been tipped for greatness by Chinese tennis great Li Na.

But despite her stunning victory and subsequent catapult into global sporting fame, the 20-year-old bashfully still said she felt flattered by the praise from Asia’s first Grand Slam singles champion.

“I think it makes me happy that Li Na talks about me!” she said.

“For me definitely I don’t want to stop at just one Grand Slam, of course I want to win more, but right now it’s not the Australian Open, it’s Singapore (that I) have to look forward to.”

Back-to-back tournaments in Tokyo and Beijing since clinching the US Open against her 23-time Grand Slam champion opponent means she has barely had time to look back at the impact of the shock triumph.

“I keep moving, I don’t really stay in one spot, I haven’t had that mental space to think I just won the US Open,” she said.

“I don’t really feel that different or that I’ve changed.”

She is now undergoing treatment for her back injury, which she said she picked up in Beijing, but said she was “excited” to play in Singapore alongside the women’s elite.

At the beginning of the year she ranked just 68 but is now within touching distance of making history as the top ranked Japanese woman.

“I’m very excited about it,” she said.

“I know that Kimiko was number four too so that means we’re tied.

“For me the year’s not done yet so I want to keep playing and see how how I can get.”