One day, she hopes to emulate her idol on the court.
In a game full of talented youngsters, Gauff is widely seen as exceptional, not least after she became the youngest player ever to reach a US Open junior final when she finished runner-up in September.
Although Gauff has only been playing seriously for about four years, she is already dreaming big.
"Overall, I want to be the best I can be and be the greatest," Gauff told CNN in New York after losing the US Open junior final to 16-year-old American Amanda Anisimova.
Gauff, who is nicknamed "Coco," comes from an athletic family. Her father, Corey, played basketball at Georgia State University while her mother, Candi, excelled in gymnastics before becoming a track star at Florida State University.
Three years ago, she won the US Tennis Association Clay Court National 12-Under title at just 10 years and three months, the youngest champion in the event's history.
At the age of 11, Gauff was spotted by Patrick Mouratoglou, Serena Williams' coach, who asked her to join his Champ'seed Foundation, which supports budding tennis stars with training and mentoring.
A year later, she won the Orange Bowl in Florida, one of the most prestigious events in junior tennis. Previous Under-12 winners include 22-time major winner Steffi Graf and former top-ranked players Monica Seles and Jennifer Capriati.
'There is only one Serena'
Frenchman Mouratoglou, who has coached Williams to 10 major singles titles since they started working together in 2012, is impressed with the young American.
"She's amazing because she's an incredible fighter and she is an incredible athlete," Mouratoglou told CNN. "She goes for her shots and takes the risks."
Although Mouratoglou didn't want to compare Gauff to Williams "because there is only one Serena," he thinks she has a bright future.
"She has a lot to learn of course, because she is very young," he said. "But if she keeps the same attitude that she has now, if she keeps her head where it should be ... if she keeps the same attitude and the same hunger for the game, I think she can go really far."
Gauff may be a future star but tennis fans won't be able to see her play a full schedule on the women's WTA tour until she is 18 years old.
That's because of the so-called "age eligibility rule" which was introduced in 1994 to prevent players from burning out at an early age, when they are not fully developed mentally and physically.
The rule is also known as the "Capriati Rule," following the rapid rise of the American teenage star, who was ranked inside the Top 10 at the age of 14 and won Olympic gold in Barcelona two years later.
However, by the mid-1990s, Capriati's career stalled amid off-court problems including arrests for shoplifting and marijuana possession charges. She later returned to win three majors and rise to world No. 1.
At 13, Gauff isn't allowed to play in any events on the WTA Tour, the ITF women's circuit, the Fed Cup or the Olympics.
When she turns 14 in March, she will be allowed to play in two WTA events. The number of tournaments she will be allowed to enter gradually increases each year until she is 18, when she will be free to compete in an unlimited number.
Although former Wimbledon champion Lindsay Davenport agrees with the age rule in principle, she feels it may also put extra pressure on young players.
"I understand what the WTA is trying to do," Davenport told reporters at the US Open. "I don't love it. I think when some of these youngsters get into a tournament, they feel even more pressure."
Nine-time Wimbledon winner Martina Navratilova said the rule could negatively impact exceptional talents such as Gauff because they aren't able to compete with the very best during much of their teenage years.
"I think they could and should ease up a little bit," Navratilova said in a news conference at the US Open. "We are trying to be the parents, and we're not the parents. It's the parents that need to say, OK, this is enough."
Gauff said she grew up watching Venus and Serena Williams and admires "their fire inside and their aggressiveness."
Just like Serena and Venus -- who have won 30 grand slam singles titles between them -- Gauff listed her best shots as her serve and her forehand while also stressing her ability to stay mentally strong.
When asked what the biggest lesson was she has learned so far, Gauff said: "trying to stay calm during the bigger moments, I am still learning. That would be my biggest challenge, trying to stay calm and enjoying the pressure moments."
Working with Mouratoglou was a revelation.
"He's helped me change so much in my game," Gauff said. "When I went there for the first time, I learnt I can't be all flat all the time, I learnt how to hit spin."
She also met seasoned pros such as France's Alize Cornet, ATP Finals champion Grigor Dimitrov and her idol Serena Williams.
"Serena, she told me to keep working hard and to keep doing what I'm doing," Gauff said. "It means a lot just to know that someone that amazing is still encouraging younger players to be better than her and be as good as her. And hopefully one day, I can meet that standard."
Just like the Williams sisters, who have pursued other interests besides tennis including starting businesses, studying and fashion and design, life is not just about hitting a yellow ball over the net for Gauff.
"I'm definitely going to go to college, but I probably will do online and just go pro," Gauff told reporters after her finals defeat at the US Open.
"My decision may change in the future, but I'll definitely be graduating with a degree. Probably won't be at the age normal people do, but it may take me a while, but I definitely will be graduating with a degree."