The revelation was made in a book by Bonita Mersiades, who worked as a senior executive at the failed Australian bid for the 2022 tournament, entitled "Whatever It Takes: The Inside Story of the FIFA Way."
Mersiades writes that Lowy was so furious with Australia's first-round exit in the 2022 vote that he decided to hire a private investigator to probe the Qatari bid.
Lowy, replaced by son Steven as head of the FFA in November 2015, was hoping to find enough evidence to strip the Gulf nation of the World Cup hosting rights, it is claimed.
Mersiades' book says the probe, entitled Project Platinum and which involved high-level investigators, was not successful as it did not unearth any evidence of corruption.
Qatar 2022 have always refuted any suggestions of corruption and the bid was cleared of wrongdoing in a report from American lawyer Michael Garcia.
Garcia's report was also heavily critical of the ethics of some of the bids involved in the 2022 race, including Qatar's and Australia's fruitless yet costly attempt.
The book also includes an interview with disgraced former FIFA President Sepp Blatter , who admitted to Mersiades that Australia had "no chance" of winning the 2022 vote.
In a claim which is likely to spark further fury in Australia, who spent up to AUS$46 million (£26 million/$37 million/€29 million) on their failed bid, Blatter said there was "never" any hope of Australia being successful.
This was largely down to the time zone and the difficulty that would provide for broadcasters and lucrative rights holders, Blatter said.
The 81-year-old, currently serving a six-year ban, said he was the only person to vote for Australia.
It contradicts a previous assertion from Germany's Franz Beckenbauer, who was thought to have voted for Australia as part of a deal with the FFA.
Blatter claimed he picked Australia after he was asked to do so by daughter Corinne, who worked for the Australian governing body in the 1990s.
"My daughter wanted me to vote for Australia so I could not go home and tell her I did if I didn’t," Blatter said.
"I knew if I didn’t vote for Australia, no-one else would and I wanted you to get at least one vote."
