FIFA said a former finance committee chief who died last year, Argentine Julio Grondona, authorised the 2008 payment which went to Jack Warner.
Warner, one of 14 people facing corruption charges in the United States over $150 million in bribes, was at the time Grondona’s deputy on the finance committee.
FIFA released a statekment after the New York Times reported that Valcke, right hand man to FIFA leader Sepp Blatter, had signed off on the payment.
Despite the denial, Britain’s Press Association news agency reported a letter from South Africa’s Football Association chief to Valcke which indicated he knew about the payment.
The South African government asked FIFA to “withhold” money intended for the organisers of the 2010 World Cup and send it to a development project in the Caribbean run by Warner, the FIFA statement said.
According to US investigators, the $10 million was a bribe promised to Warner and his deputy Chuck Blazer to secure the 2010 World Cup. South Africa has strongly denied any wrongdoing. Its football leaders have promised to hold a press conference on Wednesday to “fully address allegations”.
– Corruption battle grows –
The New York Times, quoting US investigators, said Valcke had approved the payment to an account controlled by Warner, then head of the North and Central American and Caribbean confederation (CONCACAF),
The New York Times, citing unnamed law enforcement officials, said the payments are a crucial part of the indictment against the 14 football officials and marketing executives.
FIFA said it had acted as an intermediary between South Africa and a World Cup legacy project to “support the African diaspora in Caribbean countries”.
Neither Valcke “nor any other member of FIFA’s senior management were involved in the initiation, approval and implementation” of the development project, it added.
Valcke is not among those facing charges and Swiss authorities said that they have received no US request for assistance regarding the French secretary general.
Valcke on Monday announced that he had called off a planned visit to Canada next week for the start of the Women’s World Cup. Blatter still plans to attend the final.
“The payments totalling $10 million were authorised by the then chairman of the finance committee and executed in accordance with the organisation regulations of FIFA,” added the statement.
Grondona, a controversial figure in world football over many decades, was finance committee chief at the time. He was a senior FIFA vice president when he died last year at the age of 82.
Swiss police, following a US request, arrested seven FIFA officials in Zurich two days before Blatter was reelected as president on Friday.
Blatter, who has faced calls, even since his reelection, to stand down, has expressed doubts about the raid.
But the corruption scandal has since spread with authorities in several countries launching investigations.
Brazilian prosecutors are investigating Ricardo Teixeira, former Brazilian Football Confederation (CBF) president, for money-laundering and fraud, officials said.
Jose Maria Marin, who was CBF president until April, was one of the seven people detained in Zurich. Texeira led the CBF for 23 years until 2012.
Police found that between 2009 and 2012, Texeira moved 464 million reais (about $150 million) through his accounts, the newsmagazine Epoca reported after gaining access to the police file.
Teixeira, now 67, stepped down in 2012 amid corruption allegations. He is the son-in-law of former FIFA president Joao Havelange, who was also involved in multiple controversies while head of the world body.
Paraguayan authorities have meanwhile placed the ex-president of the South American Football Confederation, Nicolas Leoz, 86, under house arrest.
Leoz is one of the 14 facing US charges and US authorities had asked for his extradition. – Agence France-Presse