The Sunday Times claimed on Sunday that Nigeria's Amos Adamu and Tahiti's Reynald Temarii had indicated their willingness to back the United States for the 2018 tournament in return for money.
The United States have since decided to focus solely on the 2022 finals. The newspaper have video evidence backing up their claim, and stressed throughout that they never claimed an official link to the United States's bid.
Temarii has pleaded his innocence, saying: "I'm confident about my integrity but I made a mistake by talking in that way".
Adamu - who was filmed asking for US$800,000 for artificial pitches to be paid to his personal bank account - has not responded.
Fifa said on Monday that as well as investigating the pair they were looking into two allegations about countries involved in bidding. It appears to revolve around trading of votes, with endorsement of a bid for 2018/2022 with reciprocal support offered.
Last week England announced their withdrawal from the race to host the 2022 tournament to focus on the 2018 finals.
It is a move widely seen as linked to United States announcing their focus on the latter tournament on the same day.
England are bidding to host the 2018 tournament, along with Russia and joint bids from Spain/Portugal and Holland/Belgium.
The United States are running to hold the 2022 finals, alongside Australia, Japan, South Korea and Japan.
Chuck Blazer, a Fifa vice-president, has suggested the allegations against Adamu and Temarii will not count against the English bid.
Lord Triesman, former chairman of the England bid, resigned in May after saying - in comments he thought were private, but which were sold to the Mail on Sunday - that 2018 rivals Spain were bidding to bribe referees during the World Cup in South Africa, and that they would consider backing out of the 2018 race and supporting Russia if they supported their attempts to influence officials.
Australia were quick to distance themselves from the investigation, with a spokesman for the Football Federation Australia saying it "has nothing to do with us".