"FIFA has opened proceedings against two current members of the executive committee to ascertain whether they have violated the code of ethics," football's governing body said in a statement on Monday.
"(FIFA) has asked the chairman of the ethics committee to act without delay to take all possible steps including the possibility of provisional measures, should the relevant conditions be met.
"Investigations are also ongoing in relation to other FIFA officials who may have been involved in the issue in question."
The ethics committee is due to meet on Wednesday.
FIFA's announcement came as the allegations threatened to discredit the bidding process, which is due to end when it announces the winners in Zurich on December 2.
The 24-strong executive committee will decide both venues on a majority vote.
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FIFA said some member associations would be investigated for "alleged agreements" which might have broken the bidding rules. It did not elaborate.
"FIFA also confirms that the alleged agreements between member associations would also be a clear violation of the bid registration document and the code of ethics," said the statement.
"Therefore, an investigation has also been opened into the member associations in question as well as their bid committees."
Britain's Sunday Times newspaper said Oceania Football Confederation (OFC) president Reynald Temarii and Nigeria's Amos Adamu - both executive committee members - had offered to sell their votes when approached by reporters posing as lobbyists for an American consortium.
The newspaper report said Adamu was filmed asking for 500,000 pounds for a personal project and that Tahitian Temarii asked an undercover reporter in Auckland for NZ$3m ($2.27 million) to fund a sports academy at the OFC's headquarters.
Adamu and Temarii both declined to comment on the matter at FIFA headquarters on Monday.
England and Russia are bidding for the 2018 finals along with joint bids from Spain/Portugal and Belgium/Netherlands. The candidates for 2022 are the United States, Japan, South Korea, Qatar and Australia.
