Mr. Valcke and Mr. Kattner did not immediately respond to FIFA’s statement.

None of the three men currently work for FIFA. Mr. Blatter was barred from soccer by FIFA in December and replaced by a new president, Gianni Infantino, in an election in February. FIFA suspended Mr. Valcke, Mr. Blatter’s longtime deputy, last fall and fired him in January amid accusations of corruption. Mr. Valcke was replaced temporarily as secretary general by FIFA’s finance director, Mr. Kattner. That effectively placed Mr. Kattner in control of FIFA’s finances in the months leading to this year’s presidential election, but he, too, was fired, in May, after FIFA said it had discovered he had breached his fiduciary duty to the organization.

The accusations by FIFA and its lawyers seemed intended to paint a picture of a leadership group operating outside FIFA financial controls:

■ In 2010, Mr. Blatter, Mr. Valcke and Mr. Kattner were awarded $23 million in retroactive bonuses for the 2010 World Cup in South Africa that FIFA said were not called for under their employment agreements.

■ In 2011, with Mr. Blatter in a contested election for the FIFA presidency, Mr. Valcke and Mr. Kattner were given eight-year contract extensions that included guarantees that they would receive full payment of their salaries if they lost their jobs, a likely outcome under a new president.

■ That same year, Mr. Blatter received a bonus of 12 million Swiss francs (about $12 million) for overseeing the 2014 World Cup.

■ In May 2015, only days after the arrests of several of their colleagues in Zurich, Mr. Blatter, who signed a contract in 2008 that paid him 2 million Swiss francs (about $2 million) a year, executed a new contract that increased his salary to about $3 million and included the prospect of another performance bonus of $12 million if he completed his term.

A day after that, Mr. Kattner’s contract was extended four years — through December 2023 — and modified to include a clause that he be paid in full even if he was fired. In its statement, FIFA dryly labeled the timing of that contract extension “noteworthy.”

The details of Quinn Emanuel’s investigation deflected attention — at least momentarily — away from two other FIFA stories this week: the news that the Swiss attorney general’s office had conducted a new raid on FIFA headquarters in Zurich on Friday as part of a continuing investigation into possible corruption, and recent issues regarding transparency that have plagued Mr. Infantino. Earlier this week, a German newspaper reported that Mr. Infantino had worked behind the scenes to marginalize FIFA’s independent auditor in a leadership power struggle.