German publication Der Spiegel claimed that convicted match-fixer Wilson Raj Perumal correctly called the outcome of Croatia's 4-0 win over Cameroon in the group stages of the Brazil showpiece in a conversation on Facebook with the magazine.
Der Spiegel also claimed that Perumal indicated to them a Cameroon player would be sent off in the first half, with Alex Song subsequently dismissed five minutes before the break.
For his part, Perumal has strenously denied those suggestions, while Der Spiegel continue to stand by their report.
But at a news conference on Wednesday, the world governing body called on the magazine to bring forward evidence to support the allegations.
FIFA's head of media, Delia Fischer, told a news conference in Rio: "We have requested Der Spiegel to provide us with all the communications with Perumal and any other material in order to prove the allegations they have made.
"So far we have no evidence of any match manipulation on the betting market. The media and other stakeholders should not call people's or organisation's credibility into question just for headlines.
"It is really important to make sure that information is handled with the necessary respect and care."
In his statement, Perumal said: "Contrary to the 'revelations' published by the German weekly Der Spiegel that were picked up by news outlets worldwide, I did not predict the result of the Cameroon v Croatia match played on June 18, 2014.
"The Facebook chat with the Der Spiegel journalist took place a few days after the match – 21 June, as confirmed by my Facebook log – and was but an informal assessment of the behaviour of the Cameroon team at the Brazil 2014 World Cup after they had played two of their three group stages matches, including the one with Croatia.
"At no time did I make reference to four goals being scored or to a red card being issued.
"At no time did I suggest that I had any way of corroborating or substantiating what was meant to be an educated guess based on my extensive match-fixing experience.
"I am shocked and amazed that a respected magazine such as Der Spiegel would go so far as to fabricate statements by yours truly with the visible aim of stirring the row over match-fixing.
"I apologise to the Cameroon FA and to its fans if I inadvertently offended them. It was not my intention."
The Cameroon Football Federation (FECAFOOT) confirmed earlier this week it had launched an investigation into the claims.
