“All the young players say they want to be No 1 but they don’t really mean it… Coco is not like that.”

Those were the words of Serena Williams’ full-time coach Patrick Mouratoglou in September last year, just two months after Cori ‘Coco’ Gauff’s emergence on the world stage at Wimbledon.

Aged 10, Gauff came to Mouratoglou’s academy in the south of France, brought by her father, seeking the assistance to help propel the American on the path to a career in the sport.

At the Australian Open, Gauff, who does not turn 16 until March, is once again creating headlines with her mature performances on the court, belying her inexperience.

Gauff beat defending champion Naomi Osaka in the third round Gauff beat defending champion Naomi Osaka in the third round Gauff beat defending champion Naomi Osaka in the third round

In just her third main draw Grand Slam singles appearance, the world No 67 is through to the fourth round in Melbourne – matching her run at Wimbledon – where she will face compatriot Sofia Kenin on Sunday.

“Some people are immature at 25, some people are mature at 15,” added Mouratoglou during a visit from Sky Sports to his academy.

“I think Coco is incredibly mature for her age.”

After winning just three games against Naomi Osaka when the pair met at the US Open last year, this time around Gauff knocked out the Australian Open defending champion in straight sets on Friday.

Gauff and Osaka could have an excellent rivalry going forward Gauff and Osaka could have an excellent rivalry going forward Gauff and Osaka could have an excellent rivalry going forward

Asked what felt different going into their third round encounter compared to the US Open, Gauff said: “Definitely a difference in the mentality entering into the match.

“I was a lot more calm and less about, you know – this match was hyped up, too. But also US Open was hyped up.

“I think now coming into this, I’m just going to have fun, play my best tennis and see what happens.”

This happened on the same day pre-tournament favourite and 23-time Grand Slam champion Serena Williams was knocked out by China’s Wang Qiang.

Serena Williams admits she was nowhere near the level of Gauff at the age of 15 Serena Williams admits she was nowhere near the level of Gauff at the age of 15 Serena Williams admits she was nowhere near the level of Gauff at the age of 15

“I was nowhere near Coco’s level either on the court or off the court, not even close,” admitted Williams.

“I was nowhere near as smart and eloquent as she is. It’s nice to see.”

Gauff is unquestionably a precocious talent, but, even if expectations should still be tempered, there is something about her that indicates she is unlikely to fall off the map of world tennis any time soon.

Gauff can reach the quarter-finals of a Grand Slam for the first time with victory against Sofia Kenin on Sunday Gauff can reach the quarter-finals of a Grand Slam for the first time with victory against Sofia Kenin on Sunday Gauff can reach the quarter-finals of a Grand Slam for the first time with victory against Sofia Kenin on Sunday

Even if her victories on the biggest stages continue to leave her in apparent utter disbelief.

“Oh my gosh. This is crazy,” Gauff said after her win over Osaka at the Rod Laver Arena. “I don’t know where that came from. Honestly, like, what is my life?”

Gauff, who won her maiden tour-level title last October, also requested to meet the court’s legendary namesake in person for the first time.

Shortly afterwards Laver tweeted: “Hello @CocoGauff – congratulations on your incredible victory tonight. I would love to meet you too.”

Can鈥檛 wait for that Selfie 馃う馃従鈥嶁檧锔忦煒?https://t.co/likluSEDyL

— Coco Gauff (@CocoGauff) January 24, 2020

It is impossible to ignore the feats of Gauff.

Not only is Gauff is performing well in singles but the 15-year-old is also forming a good doubles partnership with fellow teenager Caty McNally, with whom she has already won two doubles titles.

The American pair are through to the third round at Melbourne Park in the women’s doubles, and Gauff’s willingness to play in both events should be applauded, but more significantly it could well improve her overall game further.