By Danielle Rossingh

for CNN

(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."

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?

"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.

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.

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."

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."

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.

"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."