But withdrawing the lucrative rights to those tournaments would be a legal quagmire, say sports governance experts, and it could also call FIFA's very existence into question.
FIFA is "in completely uncharted territory," says Roger Pielke, a professor at the Center for Science and Technology Policy Research at the University of Colorado at Boulder.
He says he sees nothing in the FIFA statutes or the guidelines for running the World Cup competition that "seems to deal with any of these contingencies."
Last month, U.S. and Swiss authorities launched two separate investigations into corruption at soccer's governing body, including the bid processes for the 2018 and 2022 World Cups.
Several officials have been implicated, and the organization's president, Sepp Blatter, resigned mere days after winning a fifth straight term.
Investigators are taking a closer look at what led FIFA's member states to vote in favour of giving the 2018 and 2022 World Cups to Russia and Qatar.
Domenico Scala, the independent chairman of FIFA's audit and compliance committee, has suggested in recent days that if the investigation turns up evidence of bribery, one or both countries could lose the tournament.
Other FIFA officials have thrown cold water on that suggestion, which is telling, says Pielke.
"It's clear that there's an internal struggle at FIFA right now," he says.
Given the prestige involved in winning the bids and the money each country has invested in infrastructure to host the tournament (Qatar will reportedly spend $200 billion US in total), losing the rights would be a tremendous disappointment and undoubtedly lead to recriminations.
Withdrawing the 2018 and 2022 World Cups would be legally tricky, says Jean-Loup Chappelet, a professor of public administration at the Université de Lausanne in Switzerland with an expertise in sports governance.
Whatever the truth about the World Cup bid process, Russia and Qatar won their respective bids, and the soccer organizing committees in each country would have signed a legally binding document with FIFA agreeing on terms for hosting the event, says Chappelet.
Unlike the contracts signed by host cities for the Olympics, Chappelet says World Cup contracts are not made public, so it's impossible to know the terms.
Even so, he says it's quite likely that one of the stipulations was that in the case of a breach of contract, FIFA and the country involved would argue their respective cases in front of the Court for the Arbitration of Sport (CAS) in Lausanne.
CAS works under Swiss law, but regularly adjudicates commercial disputes between sports organizations from different countries.
Even before the current investigations, a number of sports journalists and other advocates have questioned the suitability of Russia and Qatar as World Cup hosts.
They pointed to the fact that both countries have poor human rights records. Russia has been criticized for anti-gay legislation enacted prior to the 2014 Olympic Games in Sochi, and international observers have also raised concern about racist hooliganism at domestic soccer matches.
With Qatar, arguably the biggest concerns are reports that hundreds of foreign workers from India and Nepal have died in the construction of new stadiums and infrastructure.
As well, there have been misgivings about holding soccer's premier event in a Gulf state where the average summer temperature can reach 41 degrees, which could be dangerous for players.
To avoid this potential hazard, Blatter announced earlier this year that the 2022 World Cup would defy convention and take place in the cooler months of November and December.
While the soccer world waits to find out whether FIFA will indeed withdraw the Russia and Qatar World Cups, there is already strong evidence that the awarding of previous tournaments involved corruption.
For example, a recently uncovered 2007 email sent by FIFA Secretary-General Jerome Valcke suggests that Blatter knew about a $10-million payment from South Africa's soccer federation to a FIFA official.
Many observers consider it to be thanks for giving the African nation rights to the 2010 tournament.
The FBI has also announced that it is widening its investigation of FIFA to the organization of the 2014 tournament in Brazil.
Chappelet says the long list of allegations ultimately raises doubts about FIFA's ability to carry out its single most important role, which is to study, vet and choose the appropriate venue for soccer's biggest event.
"If this awarding capacity is threatened, or put in question, the whole thing will crumble, because [FIFA's] main duty is to make sure every four years that there is a World Cup," says Chappelet.