The world soccer governing body said Friday that ethics panel chairman Claudio Sulser had decided not to pursue the matter. FIFA said it "found no indication that there is any basis to the allegations reported."
David Triesman resigned as chairman of England's 2018 World Cup hosting bid after his claims were published following a tabloid newspaper sting this month.
Triesman was recorded saying that Spain could drop its 2018 campaign and support Russia's bid in exchange for help to bribe referees at the World Cup.
FIFA said Triesman claimed the remarks were not meant as an accusation.
"Triesman explained that this speculation was not an allegation on his part but was reported to him in a private capacity," FIFA said in a statement.
Triesman told FIFA that the claim did not reflect the view of any other English soccer officials.
The FA and England's 2018 bid team had "unreservedly apologized for and expressed their bitter regret" to officials in Spain and Russia, FIFA said.
Sulser's ethics team also received statements from Spain and Russia.
FIFA said Sulser's committee would "remain vigilant to ensure that ethical conduct and fair play is respected in the bidding for the 2018 and 2022 FIFA World Cups."
FIFA's 24-man executive committee will choose the two hosts in December.
The 2018 tournament is expected to be awarded to a European bid. England and Russia are leading contenders, with joint bids from Spain-Portugal and Netherlands-Belgium.