The Gulf state are the hot favourites to become the hosts of the Men's World Cup in 2034 as the only runners for the right thus far.
Having launched an official bid for the World Cup, they could now turn their attention to the female edition, hosted a year later.
The technical director of the Saudi Arabian women's team, Monika Staab, has expressed her interest in seeing her country host the event.
"I believe it's a bright future (for the women's and girls' game in Saudi Arabia)," she said at the Leaders Week conference at Twickenham.
"I told (the sport's administrators) it takes time to go to the World Cup. (In) 2035 (sic), I know they want to host the men's World Cup.
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"Why not hosting the Women's World Cup in 2035?
"They are going to have the AFC competition, hosting in 2026, so we're now getting a team ready to be at least competing at that level."
It would be a surprise turn of events, considering that it was only 2018 when women were allowed to attend football matches.
And they could come up against England for the 2035 Women's World Cup, who are interested in hosting the event as well.
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FA chief Debbie Hewitt revealed in May that she hoped that the World Cup would be hosted on these shores in 2031.
But if the joint Germany-Netherlands-Belgium bid for 2027 is successful, as strong favourites, it would mean delaying another European bid for four years.
However, there is nothing to stop Saudi Arabia from hosting the two World Cups within a year of each other.
The Middle East country is already vying for the AFC Women's Asian Cup in 2026, competing with Australia for the right to host the event.
England reached the final of the Women's World Cup this summer in Australia and New Zealand, eventually losing to Spain 1-0.
The Lionesses had won the European Championship a year before at Wembley and women's football has seen incredible growth in the last few years.