Britain's Sunday Times newspaper said the offers had been made to its reporters who were working undercover and posed as lobbyists for a consortium of American private companies.
The report said Nigeria'a Amos Adamu was filmed asking for money for a personal project and that Oceania Football Confederatinon president Reynald Temarii from Tahiti wanted money for a sports academy.
FIFA will decide on December 2 in Zurich which countries will host the 2018 and 2022 World Cups. The choices will be made by the 24-strong executive committee
"FIFA has already requested to receive all of the information and documents related to this matter (the Sunday Times report), and is awaiting to receive this material," FIFA said in a statement.
"In any case, FIFA will immediately analyse the material available and only once this analysis has concluded will FIFA be able to decide on any potential next steps.
"In the meantime, FIFA is not in a position to provide any further comments on this matter."
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.
