Now that soccer legend Abby Wambach has retired from play, would she consider taking a top job at FIFA, the troubled soccer organization that last week handed down an eight-year suspension to former president Sepp Blatter?

Absolutely, says Wambach, though, “I doubt that they would want me—I’m not going to be the easiest person in the room.”

She may be right on that score: Wambach and a who’s who of current and former players—including Carli Lloyd, Ali Krieger, Mary Harvey and Moya Dodd—are pushing FIFA to tap the growing ranks of retired female players and put more women in leadership positions within the organization.

“You’re talking about FIFA—it’s a federation that has produced some of the most powerful women on the planet. Use them as a resource!” says Wambach, who has scored more goals in international competition than any other player, male or female. “It’s laughable that FIFA hasn’t integrated women more, especially in women’s soccer.”

According to a November New York Times op-ed by Dodd, a former Australian national team player, as well as member FIFA’s executive committee and chairwoman of FIFA’s Women’s Football Task Force, less than 1% of the voters in FIFA’s Congress are women. And that’s not all: Dodd also notes that 8% of the group’s national soccer board members are female, 7% of coaches are women, and just one member of FIFA’s 13-person reform committee is female.

In a proposal that Dodd submitted to FIFA’s reform committee, she asked the organization to commit to bringing the representation of women up to 30%. Her demands are echoed in a letter put forth in November by more than 150 athletes, coaches, and sports executives, which proposes “an immediate 30% presence of women on the FIFA Executive Committee, to be mirrored within a reasonable time at all levels of the sport.” The list of signatures on the letter include Wambach, Harvey, Lloyd, and Krieger. Also on board, Olympic diver Greg Louganis, tennis player James Blake, and (American) football player Michael Sam.

Wambach agreed to sign the petition, telling Fortune that “there’s nothing but good stuff that can come from it,” though she admits that she’s frustrated by the 30% figure. “I know you have to start somewhere, but [Dodd’s] goal of 30 is too low.” Instead, she believes FIFA should be held to 50-50 gender split—and pushed to broaden its ethnic and religious diversity as well. “If you don’t ask for something, surely they won’t give it to you.” The 30% demand, she says, “sells that remaining 20% of women short.”

Getting more women in the room

Harvey, Olympic gold medalist and goalie on the U.S. national team that won the inaugural Women’s World Cup in 1991, was a driving force behind the letter. Harvey was the first woman in management at FIFA, where she served director of development from 2003 to 2008. “In 99 out of 100 meetings, I was the only woman in the room,” she says. “When made decisions, everyone else would have one way of looking at things, but mine was very different.”

There is some indication that FIFA is already taking steps to begin to chip away at that imbalance. Last week, the organization announced that it’s accepting applications for a program that aims to put more women in senior, “decision-making” jobs at the troubled soccer organization.

This is the second year FIFA has offered the Female Leadership Development Programme, a nine-month training course that’s open to 35 women. Applications for the program, which is intended to identify and develop “strong female leaders in football,” are due by Jan. 20, 2016.

The timing of the announcement is curious—FIFA put out the call for women leaders the same day that its ethics committee handed down an eight-year suspension of Blatter and his European counterpart Michel Platini. (FIFA did not respond to multiple requests for an interview.)

An ethical question

Would more high ranking women make FIFA a more ethical organization? Dodd believes so, telling Fortune via email that gender diversity “helps eliminate the conditions where corruption and fraud can flourish.”

There is some research that supports her view. A 2015 Pew Research Center survey found that 31% of respondents believe women are more ethical in business than men are. Academic research suggests that men are more accepting of ethically iffy negotiation tactics and are more likely to engage in deception than their female counterparts. One study of Chinese companies even found that companies with higher proportions of women on their boards were less likely commit fraud or violate securities regulations.

None of that proves that a better gender balance would have stopped any of the improper or illegal business that went down at FIFA. But it does suggest that it’s worth a try.

Of course, ethics is just one relevant concern. There’s also the issue of resources—men’s soccer programs receive the lion’s share of FIFA dollars—not to mention good old sexism.

“Football has actually been a haven for derision and disrespect, even in an elite league like the [English Premiere League] where Chelsea’s doctor [Eva Carneiro, who left the club earlier this year] was frequently subjected to chants like ‘get your tits out for the lads,'” says Dodd. “You wouldn’t do it in the waiting room, or on the bus, yet this has gone on unchallenged in a world-leading competition. It’s not fun, it’s not banter—it’s deeply disrespectful and damaging.”

Next steps

In response to the proposal Dodd submitted to FIFA’s reform committee, the organization put forward a slate of proposals in early December, calling for the organization to take “concrete steps to increase the role of women in the governance of football.” Specifically, FIFA’s executive committee recommends requiring that at each confederation have a least one female council member. For now, though, that’s just a recommendation: FIFA’s Congress will vote on the committee’s proposals on Feb. 26, 2016.

“This is a big step in the right direction,” says Harvey. Assuming the recommendations pass, “now it’s about how do we implement, enforce and bring it to life.”

She also applauds the leadership development program, saying, “Anything FIFA’s doing to promote inclusion of women in decision-making roles is fantastic.” However, the real test is what happens to those women after the conclusion of the program. “Are they being let in the door? Are they getting access? If not, then how do you get there?”

“That’s how you change culture,” says Harvey. “And if there was ever an organization in need of a culture change, it’s FIFA.”