Chief executive Noel Mooney says the Football Association of Wales (FAW) retains the view that Fifa president Gianni Infantino should step down.
Infantino claimed over the weekend that he has the backing the "vast, vast majority" of world football as he laughed off questions about whether he had considered resigning over the World Cup sell-off debacle.
But Mooney says the FAW's position has not altered since it withdrew its backing for Infantino in early August.
"The governance of the global game needs to be reviewed - the system is not working for us," Mooney said.
"We were the first country globally to say that we weren't going to support his (Infantino's) re-election as president. Our position certainly hasn't changed.
"What you want from a Fifa president, for example, is that moral guardianship of the game. You want somebody who has the best interests of the game at heart at all times."
Infantino faced calls to stand down over the controversial plan – known as the Fifa Forward Enterprise (FFE) proposal - to sell off stakes in Fifa's competitions to private investors, which emerged in July.
Infantino, leader of world football's governing body since 2016, apologised to the Fifa Council over the "communication and consultation" regarding FFE earlier this month.
Uefa, the sport's governing body in Europe, said Fifa should release key documents and answer all questions relating to its governance and decision-making by a deadline of 2 November.
Speaking to BBC Wales, Mooney described the FFE project as "a classic example of poor governance, poor guardrails, poor guardianship of the game".
"As you know, Uefa have asked for a review of the documents surrounding the FFE debacle," he added.
"But for us, it's not just about the Fifa president, it's about the whole system.
"We would call for a change in the governance of football… not to have one person with as much power, for example, as the president of Fifa. It's crazy."
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