Reports have it that FIFA President Sepp Blatter is currently being questioned by representatives of the Swiss attorney general.
The attorney general’s office said in a statement that it had opened “criminal proceedings” against Mr Blatter.
It said he was being investigated “on suspicion of criminal mismanagement as well as – alternatively – on suspicion of misappropriation”.
The football body had earlier cancelled a press conference scheduled to hold on Friday at its Zurich headquarters.
The Swiss attorney general’s office said the investigation surrounds a TV rights deal Mr Blatter signed with former Caribbean football chief Jack Warner in 2005.
Mr Blatter is also suspected of “a disloyal payment” in 2011 to UEFA president Michel Platini, the statement said.