The publication had claimed the 48-year-old Singaporean had predicted the outcome of the Cameroon and Croatia World Cup tie on June 18, in a Facebook chat prior to the match.
Perumal on Tuesday released a statement denying the allegation, and said the magazine had fabricated his 'informal assessment' of the match.
"We have requested from Der Spiegel all the communications with Perumal and any other material they claim to possess in order to prove the allegations they have made in public," Fifa spokeswoman Delia Fischer told reporters on Wednesday. "The article has put the integrity of the World Cup in question which is a serious allegation."
Fischer added that the world governing body for football have found no evidence so far that any of the matches have been fixed.
"As mentioned on various occasions, Fifa has carefully monitored all 56 games to date and continue to monitor," she said. "So far we have found no indication of any match manipulation on the betting market in relation to any of the 2014 FIFA World Cup matches."On Monday, the Cameroon FA announced that they have begun investigations of their own.
Perumal, a Singaporean, is currently in Hungary under police protection and claims to have intricate knowledge of the match-fixing industry based in Singapore and Eastern Europe. He released a tell-all memoir, Kelong Kings, earlier this year.