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Fifa said in a statement that it had "opened proceedings against two members of the Fifa Executive Committee to ascertain whether they have violated the FIFA Code of Ethics," and will consider "provisional measures" if necessary.
"Investigations are also ongoing in relation to other Fifa officials who may have been involved in the issue in question," FIFA added.
A British newspaper reported on Sunday that Nigerian and Oceanian members of its executive committee had offered to sell their votes in the bidding race for the 2018 World Cup to undercover journalists posing as lobbyists.
FIFA also noted that any alleged agreements between member associations would be a clear violation of the bidding rules for the World Cup and its Code of Ethics.
"Therefore, an investigation has also been opened into the member associations in question as well as their Bid Committees," Fifa said in the statement.
The governing body did not specify which countries could be under scrutiny.
The nations in the running to host the 2018 World Cup are England, Russia, Spain-Portugal and Netherlands-Belgium. For 2022, the contenders are Qatar, Australia, the United States, Japan and South Korea.
FIFA confirmed that its Ethics Committee is due to meet on October 20.
The British newspaper The Sunday Times said six senior officials, past and present, had told reporters that paying bribes offered the best chance of landing football's showcase tournament.
It also alleged that Amos Adamu, a Nigerian member of FIFA's executive committee, asked its undercover journalists for $800 000 to endorse one of the bid candidates.
It filmed him meeting with the journalists posing as lobbyists for a United States business consortium, in which he apparently offered a "guarantee" to vote for the US bid in the 2018 event in return for cash.
The report also alleged Reynald Temarii, a FIFA vice-president and president of the Oceania Football Confederation, sought three million New Zealand dollars ($2.3m) for a sports academy.
He allegedly boasted to undercover reporters that supporters of two bid committees had already offered Oceania money to swing his vote.
FIFA president Sepp Blatter said after the newspaper report was published on Sunday that there would be an "in-depth investigation".
Adamu, a controversial figure who wields major influence over Nigerian football, is also president of the West African Football Union.
He has not responded to phone calls since the allegations emerged.
Musa Amadu, the acting secretary general of the Nigeria Football Federation, declined to comment in detail, saying "we just have to wait for the outcome of this investigation before we can issue a statement on the matter".
