The Football Federation Australia (FFA) bid – which was part-funded by A$42.5m of government money – received just one vote in the 2010 ballot as the showpiece event was controversially awarded to Qatar.

The Australian bid included a payment of A$500,000 (£326,000) to CONCACAF – the game’s governing body in Central and North America – for a stadium upgrade in Trinidad and Tobago.

But FFA chairman Frank Lowy has now claimed in an open letter that Australia asked for its money back after a CONCACAF probe found it had been embezzled by senior official Jack Warner. At the time Warner was both president of CONCACAF and a vice-president of FIFA, the game’s world governing body.

Bonita Mersiades – a former member of the Australia bid team – and Senator Nick Xenophon last week wrote to the Australian Federal Police (AFP) asking them to investigate the payment.

“The AFP is currently evaluating allegations of the misappropriation of funds from Football Federation Australia to FIFA,” said the police, in a statement.

Warner is one of 14 people arrested recently as part of a United States investigation into corruption within FIFA. The wide-ranging criminal case is probing millions of dollars’ worth of alleged bribes and kickbacks over a 24-year period. The case also led to the resignation of 79-year-old FIFA president Sepp Blatter just days after he was elected to a fifth term in office.

In his open letter concerning the failed Australian bid to host the 2022 World Cup, Lowy said: “We ran a clean bid and I am proud of that, but it wasn’t a level playing field and therefore we didn’t win it. I will always be bitterly disappointed about the outcome.”

However, Lowy has in turn been criticised by former FFA board member Jack Reilly for his handling of the bid – and for the hiring of controversial consultant Peter Hargitay, a former adviser to Blatter.

“Many things were queried when Hargitay was appointed,” said Reilly, speaking to the Australian Financial Review. “I queried that mercilessly because of his reputation, but it went ahead.”