(CNN) Hurtling down the mountain at speeds of over 80 miles-per-hour, Lindsey Vonn has never let anything get in the way of achieving her goals.

But as the greatest female ski racer of all time enters the final phase of her career, there is one target the 32-year-old former Olympic downhill champion has yet to achieve: competing against the men.

In the 1973 "Battle of the Sexes", tennis star Billie Jean King easily beat Bobby Riggs in three straight sets.

Could Vonn achieve the same?

When asked if she had beaten any of the men in training, Vonn told CNN in an interview at Roland Garros in Paris: "Yeah, not all of them, but a lot of them."

"Battle of the Sexes"

Although Vonn's request to race the men was turned down by the sport's governing body in 2012, the American is giving it one last shot this year: not just for herself but she says also for the sake of her sport.

"I've always wanted to do it," said Vonn, who attended the French Open as an ambassador for broadcaster Eurosport.

"I just want the opportunity, I want to see exactly how I would fare. Training is one thing, but racing is quite another."

Photos: Women's skiing: A long way to the top Crashing out – The life of a professional skier is far from easy. Lindsey Vonn, whose 2016-17 season has been interrupted after she suffered a broken arm in training, crashes at the women's super giant slalom in Val d'Isere, France. But injuries and crashes aren't the only problems skiers face ... Hide Caption 1 of 9 Photos: Women's skiing: A long way to the top Counting the cost – American skier Lila Lapanja (pictured) is a member of the US Alpine B Ski Team. At her level, Lapanja has to pay her own travel expenses. Considering the global nature of the tour -- which counts South Korea, Canada and Italy as some of its venues -- the costs can mount up. Hide Caption 2 of 9 Photos: Women's skiing: A long way to the top Gender bias – Meanwhile American Resi Stiegler has faced questioning about when she will take a break from skiing to start a family. Her answer is always the same: "Whenever I want!"

Hide Caption 3 of 9 Photos: Women's skiing: A long way to the top Woman's world – Male and female skiers in the French team train separately, a move implemented within the last few years to enable coaches to spend more concentrated time honing in on strategy, technical abilities, and mental preparation. This includes the likes of Tessa Worley (center), who is seen celebrating her first place finish in the giant slalom event in Killington. Hide Caption 4 of 9 Photos: Women's skiing: A long way to the top Race day – Without the stress of travel and training, race days usually offer more time for mental reflection, exploring a resort's trails, and getting in the zone. It's one of the most appealing aspect for many skiers; the adrenaline rush of events like the slalom (pictured). But then there's the ever-present press work and interviews ...

Hide Caption 5 of 9 Photos: Women's skiing: A long way to the top On camera – Media attention is impossible to avoid for top-level competitors. Tina Maze -- who retired from skiing earlier this season -- would know this better than anyone else. The Slovenian competed in the Alpine Skiing World Cup for 15 seasons, winning 26 events and one overall title in 2013. Hide Caption 6 of 9 Photos: Women's skiing: A long way to the top Guess who? – It can be difficult for professional skiers to create their own public image behind the lycra, helmets, and goggles. But the likes of Mikaela Shiffrin (pictured) have taken to social media to try and connect with a wider audience. Hide Caption 7 of 9 Photos: Women's skiing: A long way to the top Sport's cutest prize? – Shiffrin has enjoyed a storming start to the season after slalom wins in Levi, Finland, and Killington, USA, topping the overall standings with 325 points. After victory in Levi, Shiffrin, like the male champion, was gifted a reindeer. Hide Caption 8 of 9 Photos: Women's skiing: A long way to the top Small price to pay? – The spectacular venues the Alpine Skiing World Cup visits are a pay-off for the hard work skiers must put in behind the scenes. "It's a great life because you travel a lot and do what you love," says Tessa Worley. "You can see great things, great places." Pictured is Crans-Montana, a Swiss ski resort that will host the tour in February 2017. Hide Caption 9 of 9

Vonn would prefer such a race to take place during the World Cup in the Canadian resort of Lake Louise, Canada.

Often nicknamed "Lake Lindsey" because Vonn has won 18 out of a total of 77 World Cup titles in the Alberta resort, she believes it would provide the best level playing field because both genders race on almost the same course.

Although Vonn is one of America's best-known female athletes, ski racing is a small sport.

With the Winter Olympics taking place in February 2018 in Pyeonchang, South Korea, what better time to stage a "Battle of the Sexes" style ski race reminiscent to the match between King and Riggs that attracted a television audience of 90 million viewers worldwide and helped put women's tennis on the map?

King's victory over Riggs at the Houston Astrodome in 1973 was watched by more than 30,000 spectactors and over 90 million on television worldwide.

"Every Olympic cycle there is definitely more excitement about ski racing," said Vonn, who in the past has been in touch with King about staging a ski race against the men.

"And this is a time when we need to capitalize our viewership and hopefully keep more fans tuning in and watching and continue to try to get ski racing on television in the US as well, outside of the Olympics."

In 2015, King told CNN that four decades on from her landmark match against Riggs, attitudes in tennis sometimes appeared to have barely moved an inch.

Vonn says the reaction from the male ski racing community has been largely positive to her idea.

Stumbling blocks

In order to measure herself against her male competitors, Vonn will have to get over a few stumbling blocks.

In 2012, the International Ski Federation (FIS) turned down her request to race her male competitors in Lake Louise, saying "one gender is not entitled to participate in races of the other" with no exceptions made.

Two weeks ago, women's chief race director Atle Skaardal called the issue "a very difficult topic" in a statement on the FIS website following the governing body's spring meetings.

Vonn racing at Lake Louise in 2012

Although he didn't reject the idea outright, and said he was waiting for the US Ski Association to come up with a concrete proposal, Skaardal said it would be "a very difficult challenge to find a reasonable way of doing this."

"Because one point that everyone is underestimating, is that we need to have equal rights for everyone," said Skaardal, a former ski racer from Norway.

"So if the ladies are allowed to race with the men, then also the men need to be authorized to ski with the ladies. And I'm not sure this is a direction we want to go."

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Vonn rejected his argument.

"No man is going to want to race with the women," she said. "It's a fair argument, but I think it's probably not a necessary one.

"I am sure there is a way to make an exception. I'm sure there is a way to figure out how to allow me to do it without disrupting the rights of everyone else."

Photos: An ongoing "Battle of the Sexes" Billie Jean King has been a pioneer in the fight for equal rights in sport since starting her professional tennis career in 1959. She was rewarded for her tireless campaigning by President Barack Obama, who awarded her the Presidential Medal of Freedom in the East Room of the White House in 2009. Hide Caption 1 of 10 Photos: An ongoing "Battle of the Sexes" King (then Moffitt) plays a forehand volley during her Wimbledon semifinal in 1964. She would win her first major title at the All England Tennis Club in 1966. Hide Caption 2 of 10 Photos: An ongoing "Battle of the Sexes" King won half of her 12 career majors at Wimbledon, between 1966 and 1975. She was also instrumental in the formation of the Women's Tennis Association in 1973 that battled for equality in the sport. Hide Caption 3 of 10 Photos: An ongoing "Battle of the Sexes" in 1973, King agreed to play former world number one Bobby Riggs in a clash that was dubbed the "Battle of the Sexes." With $100,000 up for grabs for the winner, a television audience of millions tuned in. Hide Caption 4 of 10 Photos: An ongoing "Battle of the Sexes" Riggs, then retired and aged 55, had made a fortune gambling on his own matches during his career, and had beaten Margaret Court before playing King. He lost in straight sets. Hide Caption 5 of 10 Photos: An ongoing "Battle of the Sexes" Riggs and King embrace after the match at Houston in 1973. King said had she not won she would have "set us back 50 years." Hide Caption 6 of 10 Photos: An ongoing "Battle of the Sexes" King says there is still some way to go to alter attitudes in tennis. She told CNN a New York Times article on the body shape of world No.1 Serena Williams this year drove her crazy: "So what? stop evaluating us. I mean, she is probably the all-time great. So stop it. Talk about her accomplishments." Hide Caption 7 of 10 Photos: An ongoing "Battle of the Sexes" King, along with ex-husband Larry, set up World Team Tennis, a professional league with a team format, in 1973. Here she is joined by a cast of players present and past at a charity day -- including Lindsay Davenport, Andy Roddick, Serena Williams, Anna Kournikova, Tommy Haas and Jan-Michael Gambill -- as well as pop star Elton John. Hide Caption 8 of 10 Photos: An ongoing "Battle of the Sexes" King, in her role as captain of the United States Fed Cup team, gives a pep talk to Monica Seles during a 2000 tie against Belgium. She led the U.S. to four titles during her reign and was handed the Fed Cup Award of Excellence in 2010. Hide Caption 9 of 10 Photos: An ongoing "Battle of the Sexes" WTA founder King is flanked by Maria Sharapova and Serena Williams at a special gathering of former world No.1s to mark the 40th anniversary of the organization. Hide Caption 10 of 10

Svindal, Jansrud behind Vonn

Although Vonn said she had discussed legal options with her father, who is a lawyer, she said it would probably take too long and may only be decided long after her career is over.

"If for some reason we can't accomplish it, then an exhibition-style race would probably be the only option," she said.

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"I would still like it to be in Lake Louise," she added. "Lake Louise and the Canadian federation there are 100% behind me.

"So if we can somehow find a way at a similar time to when the men would be coming up there, than we would put this exhibition on."

The response from the male ski racing community has been largely positive, she said, with Olympic champions Aksel Lund Svindal and Kjetil Jansrud of Norway and American Steven Nyman "all 100% behind me."

"The number one thing is that everyone believes it would be great for the sport," she said.

"It's just a smart play. It's obviously my own personal ambition, but it helps everyone. There is no downside."