Lowy's petition has been prompted by the increasing possibility that FIFA will switch the 2022 World Cup in Qatar from the northern hemisphere summer to the winter months, and the FFA chairman wants the world governing body to delay its decision on adjusting the timing.
Qatar was awarded the 2022 event in controversial circumstances in December 2010, with Australia's bid scuppered when they received just one vote at the first stage of the ballot.
FIFA has recently indicated it would seek to move the event from its traditional date of the northern hemisphere summer to the northern hemisphere winter, a date which would clash with most of the world's biggest leagues.
It was expected to vote on the change at its Executive Committee on October 3 but Lowy believes that there are too many outstanding issues surrounding the event for a decision to be made now.
Lowy has suggested that the decision be delayed in order to properly assess the effect such a change would have on domestic football leagues around the world and to determine if compensation would be required to those leagues, which have to make substantial adjustments.
The 82-year-old Australian businessman also said any decision cannot be made until the FAFA Ethics Committee completed its inquiries into the awarding of the 2022 World Cup to Qatar.
But he also suggested that given the goalposts on when the event will be hosted have been moved, those nations who bid on the 2022 event, thinking it would be held in summer, should be compensated.
Australia famously spent 45 million Australian dollars of government money on the failed 2022 bid after initially bidding for the 2018 and 2022 World Cup.
"Australia invested heavily in the World Cup process and the entire nation was behind the bid," Lowy said on Tuesday.
"Since December 2010 Australia has been careful not to let its misgivings about the process be interpreted as sour grapes.
"But now, with increasing speculation about a change that will impact on us as one of the bidding nations, and because our competition will be affected, we have made our position public."
Lowy had already taken his concerns to FIFA president Sepp Blatter in a letter in July.
"If the World Cup were to be staged in the middle of our A-League season it would impact on our competition, not just for 2022, but for the seasons leading up to and beyond that date.
"Clubs, investors, broadcasters, players and fans would all be affected.
"FIFA has an opportunity now to make the best of a bad situation by embarking on a transparent and orderly approach, unlike the process that led to the original flawed decision in December 2010.
"FIFA champions the notion of 'Fair Play' and that principle should apply to the decisions it makes in the coming months."
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