By Barry Moody
It said it would not pursue the matter further.
The affair is believed to have badly damaged England's bids for both the 2018 or 2022 World Cups.
Triesman, former chairman of the English Football Association as well as the bid committee, quit earlier this month after a British newspaper published his secretly-recorded comments suggesting the two rival bidders were planning to bribe referees at the World Cup starting here on June 11.
A FIFA statement said that Triesman had spoken of speculation circulating among journalists.
It quoted him as saying the speculation did not reflect any information known to him or the English authorities and his comments were not intended to be taken seriously.
FIFA said it had also contacted football authorities in both Spain and Russia, to which the English FA has profusely apologized for the statements made by Triesman.
In light of the lack of any evidence supporting the allegations "the chairman of the FIFA Ethics Committee has decided not to pursue this matter any further," the statement said.
Earlier, FIFA said it had tightened safeguards against match-fixing at the World Cup, including setting up a confidential hotline for players, coaches and referees to report attempts to bribe them.
Matches would also be monitored by Early Warning System (EWS), a company formed to monitor signs of matching fixing, while 400 bookmakers would report any irregular betting.
FIFA Secretary General Jerome Valcke has said it is vital that there could be no suggestion of bribery or corruption at soccer's biggest event.
(Editing by Alison Wildey)