Domenico Scala, the independent chairman of its audit and compliance committee, told a Swiss newspaper that the selection process could be invalidated if evidence should emerge that the decisions came about thanks to bought votes.
His comments came after undercover recordings released by The Sunday Times cast further doubt over the bidding process which led to South Africa being chosen to stage the 2010 tournament.
Ismail Bhamjee, a Fifa executive committee member, was recorded claiming that he believed Morocco had in fact, won more votes than South Africa, who went on to host the 2010 competition, but FIFA manipulated the results of the secret ballot.
Question marks over the process which led to the historic 2010 tournament, the first to be staged in Africa, now centre on a $10 million (£6.5 million) payment by the South African government said to support a project to support the African diaspora in Caribbean countries.
The money, which has been described as a "bribe" to help secure the tournament, was sent from Fifa to an account controlled by its disgraced former Vice-President Jack Warner following a request to the secretary general Jérôme Valcke, from the South African Football Association.
Last week Fifa insisted that neither Mr Valcke nor any other member of Fifa's senior management were "involved in the initiation, approval and implementation" of the deal.
In the email, dated December 7 2007, Mr Valcke appears to be chasing a South African government minister over the payment.
"I have never received confirmation but more important I would like to know when the transfer can be done," he wrote.
Crucially, he went on to remind the recipient that the plan was: "Based on a discussion between Fifa and the South African government and also between our President and HE President M'Beki (sic)."
The message refers to an earlier letter, signed letter of September 19 2007, in Mr Valcke details the South Africans' commitment to paying $10m to a legacy programme for Africans living in the diaspora "and specifically for the Caribbean Countries".
But a spokeswoman for Fifa insisted the messages show did not prove that Mr Valcke and Mr Blatter were involved.
"It is simply referring to an update given by the then President of South Africa to the FIFA President about the South African government's formal request," she said.
"That constitutes information, not involvement.
"As previously stated and confirmed by the South African authorities, this programme was initiated by the South African government for the Caribbean and it was publicly announced by them at the time."
She added: "He was aware of but did not initiate the transfer.
"The transaction was authorised by the then chairman of the Finance Committee."
Later correspondence between Fifa and the South African Football Association stipulate that the money should be paid to accounts controlled by former Fifa vice president Jack Warner, who headed the Caribbean football association.
The FBI, which has launched a probe into alleged corruption by a string of Fifa officials and issued warrants for the arrest of Mr Warner along with eight others, has alleged that the payment constituted a bribe in exchange for his support for the South African bid, and that Mr Warner took much of the money for his personal use.
Senior sources in football have credited Mr Blatter's decision to step down last week to the leaking of such internal documents that may eventually implicate him.
South Africa's government has confirmed it authorised the payment. But its sports minister has angrily rejected suggestions it was a bribe, saying those behind them had racist and political aims including "a thinly veiled offensive against South Africa's right to determine her own foreign and domestic policy".
Mr Mbeki, who was ousted from the presidency in 2008 by the now President Jacob Zuma, has denied the government paid a bribe to host the world cup but has not spoken about the specifics of the allegations or his involvement in the payment.
South Africa's sports minister initially suggested reports Mr Mbeki was directly involved in the plan were "defamatory" but last week confirmed that as head of state at the time, it was his idea.
Mr Mbeki's spokesman did not return requests for comment yesterday.
South African opposition parties have called for the country's football chiefs to be called before parliament to answer questions about the payment, and subsequent emails which suggest its method of transfer was designed to keep it secret.
Three days after Mr Valcke's email to South Africa's deputy finance minister chasing payment, Danny Jordaan, the head of the 2010 World Cup organising committee, wrote to Mr Valcke addressing him as "My Friend" and confirming the money would be paid.
Mr Jordaan said that instead of paying it directly however, Nkosazana Dlamini-Zuma, the then foreign minister and now the African Union chairman, had suggested the government pay the money to the organising committee, and Fifa pay the money to the Caribbean project then deduct it from the money it would pay the host nation in the years to come.
