Qatar beat bids from Australia, Japan, South Korea and the United States to win the right to host football's showpiece tournament despite temperatures in the Gulf nation reaching 50°C in the middle of the year.
After heavy criticism of the decision, calls were made to move the tournament from its normal date to the end of the year when temperatures in Qatar are lower.
Lowy, the billionaire owner of the Westfield shopping centre empire, said a quick decision over the move at FIFA's executive board meeting next month risked "making a bad situation worse".
As well as the other bidders, Lowy said countries with professional leagues, such as Australia's A-league - which would be disrupted by the move - should also be compensated. "Our season takes place during the Australian summer to avoid a clash with other local football codes," said Lowy. "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."
Fox, part of Rupert Murdoch's 21st Century Fox entertainment group, echoed that concern. The broadcaster paid an estimated $425m for rights to the 2018 and 2022 World Cups, outbidding rivals ESPN.
A Fox statement read: "Fox Sports bought the World Cup rights with the understanding they would be in the summer as they have been since the 1930s."
Sepp Blatter, the FIFA president, last week stood by the decision to award the World Cup to Qatar, saying the decision to play it in the middle of the year was the only mistake.