World soccer's governing body had expected to allocate the 2026 tournament to a host nation in 2017, with the bidding process to start soon, Valcke said, but in the current situation, it's "nonsense to start any bidding process for the time being."
FIFA said Monday that there are no legal grounds for it to take the 2018 World Cup from Russia or the 2022 event from Qatar.
Speaking to reporters while on a visit to Russia on Wednesday, Valcke said preparations for hosting the 2018 World Cup were "on track."
FIFA has been embroiled in scandal since the United States indicted 14 people, including nine top FIFA officials, on corruption charges last month. Swiss authorities simultaneously opened a separate investigation into how the 2018 and 2022 World Cup were awarded.
The U.S. indictment accuses Jack Warner, FIFA's former vice president and a member of parliament in Trinidad and Tobago, of taking a $10 million bribe to vote for South Africa to host the 2010 World Cup. The indictment says South Africa was willing to pay $10 million to the Caribbean Football Union "to support the African diaspora" in exchange for Warner's and two other conspirators' votes to put the 2010 World Cup in South Africa, instead of Morocco. The South African bid committee has denied any impropriety in the payment.
Valcke: 'It was not FIFA's money'
Valcke also strenuously denied any wrongdoing in connection with the $10 million payment.
He said Wednesday that he had signed off on the transfer of funds from South Africa to the Caribbean Football Union, as it was in line with the rules, but that the money was not FIFA's and that the global body could not control how its members dealt with funds.
"Why is it FIFA who has to explain the misuse of the money? It was not FIFA's money. We have nothing to do with this money. I have no more answer about this case," he said.
He also insisted that FIFA "has never been described as a corrupt organization" and that every penny it spent of its own funds was closely audited.
Valcke suggested that the media was out to bring him down, after the announcement by FIFA President Sepp Blatter last week that he would resign as the body's head.
"You have decided that after Blatter, I have to be the head to cut," he said to the gathered reporters.
Russia has insisted that its right to host the World Cup in 2018 is not in question.
Speaking alongside Valcke, Russian Sports Minister Vitaly Mutko said his country was "acting in the framework of the legislative basis" when it made its winning bid and had nothing to hide.
"I don't see any threats to our championship because we have worked, we really know what we're doing. We want to leave behind something that is great for the future," he said.
Claims of rigged voting process
The Sunday Times of London reported
over the weekend that secret tapes exposing the rigged voting process for the 2010 Cup were suppressed by FIFA and Blatter, until their release last week.
The BBC reported Sunday
that documents show three wire transfers totaling $10 million from FIFA to accounts of the Confederation of North, Central American and Caribbean Association Football, which were controlled by Warner, beginning in the winter of 2008. Then, the documents suggest, Warner used that money for cash withdrawals, personal loans, and to launder money, the BBC reported.
There was no immediate response from Warner to those reports in British media.
In all, U.S. prosecutors allege FIFA officials took more than $150 million in bribes to provide "lucrative media and marketing rights" to soccer tournaments.