Football`s governing body revealed the contracts of ex-president Blatter, fired ex-secretary general Valcke and sacked former finance director Kattner one day after a Swiss police raid.
Its lawyers said there was evidence that the trio made "a coordinated effort" to "enrich themselves" between 2011 and 2015.
Documents and electronic data were seized during Thursday`s operation, which relates to investigations into Blatter and Valcke.
Suspected of criminal mismanagement of Fifa money, Blatter and Valcke were banned for six and 12 years respectively by the governing body`s ethics committee in February. Both deny wrongdoing.
A statement for the Office of the Attorney General of Switzerland (OAG), which carried out the investigations, read: "Documents and electronic data were seized and will now be examined to determine their relevance to the ongoing proceedings."
Fifa said the evidence uncovered by its own internal investigation would be shared with the Swiss Attorney General`s office and the US Department of Justice.
Richard Cullen, Blatter`s lawyer, said: "We look forward to showing Fifa that Mr Blatter`s compensation payments were proper, fair and in line with the heads of major professional sports leagues around the world."
Meanwhile, Blatter`s long-time public relations advisor Klaus Stoehlker told BBC Sport he would be ending their professional relationship, adding: "The Fifa volcano is exploding now."
Fifa has been in turmoil since May 2015, when a US investigation exposed widespread corruption at the top of the organisation.
Fifa: Sepp Blatter, Jerome Valcke & Markus Kattner `awarded themselves
04 June 2016
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Former high-ranking Fifa officials Sepp Blatter, Jerome Valcke and Markus Kattner awarded themselves pay rises and bonuses worth $80m (
