A person familiar with the cases confirmed the names Thursday to The Associated Press after the five were identified in European media reports. The person spoke on condition of anonymity because the FIFA probe is confidential.
The current FIFA board members under investigation are FIFA vice-president Angel Maria Villar of Spain, Michel D'Hooghe of Belgium and Worawi Makudi of Thailand.
Villar and Makudi risk losing their FIFA seats within months as even provisional suspensions from all football duty can block them standing in scheduled confederation elections.
The others under suspicion are German great Franz Beckenbauer and Harold Mayne-Nicholls of Chile.
Beckenbauer was a FIFA voter when the board chose Russia to host the 2018 World Cup and Qatar secured the 2022 tournament. He was provisionally suspended during the World Cup in June for initially refusing to help Garcia's probe.
Mayne-Nicholls inspected the bids for FIFA ahead of the December 2010 polls, and reportedly sought placements for family members at Qatar's influential Aspire youth academy.
Last week, FIFA ethics committee chairmen Michael Garcia and Joachim Eckert said "a number of formal cases" had been opened against unidentified individuals.
FIFA also filed a criminal complaint to Swiss federal prosecutors against unnamed individuals cited in Garcia's investigation report, adding to a sense of disarray about the wider World Cup investigation.
The probe was revived after Eckert tried to close the cases against Russia and Qatar — a decision Garcia quickly appealed to FIFA.
On Thursday, FIFA said it "cannot confirm or deny any such information" about the five named, and referred questions to the ethics panel. The Kirkland & Ellis legal firm in Manhattan where Garcia is a partner was closed Thursday for the Thanksgiving holiday.
Individuals were identified Thursday despite strict confidentiality rules in FIFA's code of ethics sealing details of who is under investigation, and for which alleged offences.
FIFA President Sepp Blatter has backed Eckert's view that evidence in a 430-page report submitted by Garcia's investigations team cannot be disclosed. They cited privacy rights to protect suspects and witnesses.
Some members of FIFA's board who joined since the World Cup votes are calling for full disclosure. Garcia and UEFA President Michel Platini want "appropriate publication" with some redactions.
Villar, who was elected to FIFA's ruling board 16 years ago, was a leader of the Spain-Portugal bid that was among four candidates in the 2018 contest. It lost despite a widely reported voting pact with Qatar, in breach of FIFA rules to prevent collusion.
A former Spain player and chairman of FIFA's legal committee, Villar was previously identified in March as trying to remove Garcia from the investigation.
One bidder was "particularly unco-operative" with Garcia's requests, Eckert noted in his investigation summary. Only Spain-Portugal among nine bidders was not examined in Eckert's 42-page document.
D'Hooghe, the longest tenured board member with 26 years' service, previously acknowledged accepting a painting from a Russian former FIFA colleague during the campaign. He has said he voted only for his native Netherlands-Belgium bid in the 2018 contest.
D'Hooghe, whose FIFA mandate expires in 2017, did not respond to messages requesting comment Thursday.
Makudi joined FIFA's board in 1997 and was a longtime ally of Mohamed bin Hammam, the now-disgraced Qatari who was a key FIFA power broker.
Makudi was alleged in Britain's Parliament to have sought favours from England's failed 2018 bid. He denied the claims, which a FIFA ethics panel dismissed in 2011 before Garcia and Eckert were appointed.
Even if the FIFA prosecutions fail against Villar and Makudi, the cases could potentially remove them from high office.
Garcia and Eckert typically impose provisional suspensions on football officials when cases are pending, and both board members are due for re-election.
Villar has a late-January deadline to declare in UEFA elections for four of its eight delegates on the FIFA board. The vote of European football federations is March 24 in Vienna.
Makudi's latest four-year mandate from the Asian Football Confederation also expires soon. Those elections are expected in May.
The FIFA board, likely including the implicated trio, meets Dec. 18-19 in Marrakech, Morocco, and could get the Garcia dossier to review.
Amid the turmoil last week, Garcia and Eckert agreed that FIFA's independent audit and compliance official, Domenico Scala, should decide what evidence to give the board to help decide next steps in a saga that has dogged football's governing body for more than four years.