Soccer’s world governing body is in 'disarray' according to English FA chairman Greg Dyke
Criminal proceedings were opened on Friday against FIFA President Sepp Blatter with UEFA President Michel Platini also implicated in the long-running scandal.
The Swiss attorney general said Blatter is suspected of criminal mismanagement or misappropriation over a TV rights deal he signed with former Caribbean football chief Jack Warner in 2005.
He is also suspected of "a disloyal payment" in 2011 Platini - the favourite to succeed Blatter - for work carried out by the Frenchman more than nine years before between 1999 and 2002.
"What is clear is that FIFA must be in disarray," said Dyke, a vocal critic of Blatter in the past.
"Last week their general secretary got suspended and this week the president is being interviewed by police."
The chief executive of England's Professional Footballers' Association Gordon Taylor has also weighed into the argument, insisting that FIFA is not fit for practice.
"This just shows that football might be the best game in the world but the governance is one of the worst. If it was a school it would be under special measures," he said.
"It's not fit for practice at the moment. The biggest and best game in the world deserves better - and it's got to do better. There are enough ethical people out there to make sure the job's done properly.
"We need to look at the people, transparency and governance. It needs a whole new broom from top to bottom."
Blatter's American lawyer Richard Cullen insisted "no mismanagement" had occurred.
Cullen said in a statement: "Mr Blatter is cooperating and we are confident that when the Swiss authorities have a chance to review the documents and the evidence they will see that the contract was properly prepared and negotiated by the appropriate staff members of FIFA who were routinely responsible for such contracts, and certainly no mismanagement occurred."
Platini said he had clarified matters about the payment with the Swiss authorities after being interviewed as a witness.
"Regarding the payment that was made to me, I wish to state that this amount relates to work which I carried out under a contract with FIFA and I was pleased to have been able to clarify all matters relating to this with the authorities," the Frenchman said.