British newspaper Sunday Times said the offers were made to two of its reporters who were working undercover and posed as lobbyists for a consortium of American companies.
The paper showed a footage in which Amos Adamu, a Nigerian member in FIFA's executive committee, appeared to have asked for money to endorse the US bid.
Reynald Temarii, president of the Oceania Football Confederation, is also alleged to have asked for a payment to finance a sports academy.
"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," the world governing body 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."
FIFA will decide on December 2 which countries will host the 2018 and 2022 World Cups.
The 2014 edition will take place in Brazil.