The host of the 2027 tournament has not yet been decided with a joint USA-Mexico bid, South Africa, Brazil and a joint Belgium-Germany- Netherlands bid all in the running
The Gulf kingdom has already lodged a formal bid to host the 2034 men's World Cup.
"I believe it's a bright future (for the women's and girls' game in Saudi Arabia)," said Monika Staab at the Leaders Week conference at Twickenham.
Saudi Arabia has been accused of human rights abuses and same-sex sexual activity is illegal.
There are also concerns over women's rights in the county.
Many women's football players are open about their sexuality, with several critical of plans for tourism authority Visit Saudi to sponsor the 2023 World Cup in Australia and New Zealand.
Those plans were eventually abandoned by Fifa after the host nations expressed their disappointment with the idea.
Amnesty International Australia campaigner Nikita White said in February: "It would be quite the irony for Saudi's tourism body to sponsor the largest celebration of women's sport in the world when you consider that, as a woman in Saudi Arabia, you can't even have a job without the permission of your male guardian."
Saudi Arabia is already in the running to host the AFC Women's Asian Cup in 2026 with Australia also bidding for the tournament.
The Saudi Arabia women's team were formed in 2022 and have not played in a competitive tournament.
"I told [the sport's administrators] it takes time to go to the World Cup. I know they want to host the men's World Cup - why not host the Women's World Cup in 2035?" said Staab.
"We're now getting a team ready to be at least competing at that level."
It is possible any Saudi bid could be up against England for the right to host the 2035 tournament.
Football Association chair Debbie Hewitt told The Times in May that the governing body was considering a bid for the 2031 tournament.
However, if the joint Germany-Netherlands-Belgium bid for 2027 is successful, then the FA would have to look at delaying until 2035 because of the rotation of hosting between continents.
Saudi Arabia has invested heavily in sport in recent years and has been accused of using events to 'sportswash' its reputation.
Women's rights campaigners have been imprisoned, despite some reform under crown prince Mohammed bin Salman, such as an end to the ban on women driving.
The death penalty remains a possible punishment for same-sex sexual activity.
Several high-profile male players, including Cristiano Ronaldo and Neymar, currently play in the Saudi Pro League.
Qatar, on the border of Saudi Arabia, came under criticism for its hosting of the 2022 men's World Cup.
-- Courtesy of BBC Sport