FIFA announced on Wednesday it was also seeking repayment of salaries and a full audit of a former top official it says has continued to live an "extravagant lifestyle" while on bail from a New York Court.
The Swiss-based body, its global administration shaken by graft charges and tales of lavish spending that toppled its former head, said its U.S. lawyers had filed a restitution request on Tuesday with federal prosecutors in New York.
In the document and an accompanying letter published by FIFA, it demanded return of salaries and payment of compensation for damage to its brand, business interests and reputation.
"The defendants grossly abused their positions of trust to enrich themselves...(and have) deeply tarnished the FIFA brand and impaired FIFA's ability to use its resources for positive actions throughout the world," the document said.
It listed several cases of alleged wrongdoing, including the race to host the 2010 World Cup, won by South Africa, which had already been detailed by U.S. authorities in December.
It said that former executive committee members Chuck Blazer, Jack Warner, plus other individuals, engineered a $10 million (£7.1 million) payoff in exchange for executive committee votes.
Warner, who is fighting extradition from Trinidad and Tobago after being indicted in the U.S., had previously accepted a bribe to vote for Morocco in the 1998 World Cup hosting race, won by France, the report said.
"It is now apparent that multiple members of FIFA’s Executive Committee abused their positions and sold their votes on multiple occasions," the report said.
However, it did not mention the 2018 and 2022 World Cup tournaments which were awarded to Russia and Qatar respectively, a decision which has sparked a criminal investigation by Swiss authorities.
Ex-officials who have pleaded guilty have already agreed to pay more than $190 million in forfeiture, according to U.S. authorities.
"These funds should be used to compensate the victims of the defendants’ crimes, particularly FIFA and its member associations and confederations," FIFA said.
The very future of FIFA has been put in question by the scandal, with some demanding its abolition and replacement. The move for recompense casts FIFA for the first time, under its new president, prominently as plaintiff and victim.
FIFA is also asking U.S. officials for an audit of the assets of Jeffrey Webb, a former president of CONCACAF, which governs football in North and Central America and the Caribbean.
FIFA THE VICTIM
FIFA lawyers wrote in a letter to U.S. prosecutors that Webb, who is charged in alleged bribery schemes, was living an "extravagant lifestyle" that included an expensive, casino-themed birthday party for his wife since his release on bond.
A lawyer for Webb declined to comment on the party, which was the subject of a report last month by the Cayman News Service. Webb is from the Cayman Islands.
"FIFA as the world governing body of football wants that money back and we are determined to get it no matter how long it takes,” said FIFA's recently-elected president Gianni Infantino in a statement.
"These dollars were meant to build football fields, not mansions and pools; to buy football kits, not jewellery and cars; and to fund youth player and coach development, not to underwrite lavish lifestyles for football and sports marketing executives."
In all, 42 sports officials, executives and corporate entities have been charged in the United States under U.S. bribery and money laundering laws. The defendants include former members of FIFA's all-powerful executive committee and former heads of national and continental governing bodies.
FIFA's ethics committee banned Blatter for six years, and last month FIFA elected Infantino and enacted changes to its governance structure in an attempt to stamp out corruption.
FIFA also said it had incurred substantial legal costs and was entitled to restitution for its attorney fees and similar costs that directly flowed from the investigations.
(Reporting by Brian Homewood in Zurich and David Ingram in New York)