Fifa's disgraced former president Blatter, former secretary general Jerome Valcke and former finance director Markus Kattner are alleged to have made a "coordinated effort" to arrange the lucrative compensation by the lawyers conducting the organisation's internal corruption probe.
Read more: Fifa offices raided by authorities...again
Kattner was sacked by Fifa last week following their discovery of a secret payment scheme, while Blatter and Valcke were banned from football for six and 12 years respectively on suspicion of criminal mismanagement. Both deny wrongdoing.
"The evidence appears to reveal a coordinated effort by three former top officials of Fifa to enrich themselves through annual salary increases, World Cup bonuses and other incentives totalling more than CHF 79m (£55m) - in just the last five years," said Quinn Emmanuel partner Bill Burck.
The law firm has highlighted around £25m worth of bonuses paid to Blatter by Fifa's compensation wing between 2010 and 2015, including an £8m "performance bonus" received just three days before he agreed to step down as president in June last year.
The governing body's Zurich offices were raided and documents and electronic data seized by Swiss authorities on Thursday as part of their investigation into Blatter and Valcke, after Quin Emmanuel passed on its findings to the Swiss Attorney General and US Department of Justice.
Blatter was banned from the organisation he led for 17 years as president in December, after being found guilty of Fifa rules regarding conflict of interest and loyalty for making a £1.4m payment to former Uefa president Michel Platini that the pair said was for work carried out nine years earlier.
The 80-year-old never disclosed his remuneration while president of Fifa, only hinting that it was a little over $1m.
Fifa elected Swiss-Italian lawyer Gianni Infantino to be Blatter's replacement as president in February, on promises of large reforms.
However the organisation has already courted controversy under his leadership after its Congress passed a resolution to give the Infantino-led Council the power to dismiss and appoint members of its independent ethics committee.