Police in Brazil were told Pat Hickey was the “big chief” of ticketing for the Olympic Council of Ireland (OCI) during a meeting with two executives on Thursday night.
Chef de Mission Kevin Kilty and CEO Stephen Martin spoke to police in Rio for four and a half hours on Thursday.
Their colleague Honorary General Secretary Dermot Henihan, met with police on Tuesday.
Ronaldo Oliveira, head of specialised operations units with the Civil police, told reporters after the meeting that the men are witnesses, not suspects.
He said that police continue to hold their passports but the men will “most likely” see them returned in the coming days.
Mr Oliveira said: "The two testimonies were very good; they fully collaborated with the investigations. We will continue the investigations, and forensics. Investigators are very happy with the testimonies given today. Soon, we will have more actions. They were here as witnesses, important witnesses.
"They collaborated and confirmed the participation of Patrick Hickey as the big chief of this operation. All practices are determined by him. We were able to put together the jigsaw and we’ll soon have more actions.”
He said police are “going to intensify” investigations.
“Tomorrow we will be joining together forensics. We’ve already activated the money laundering arm. Interpol has already been activated."
Asked when he will return the men's passports Mr Oliveira said: "We are going to put together other evidence and emails. Then we will decide whether to solicit the return of their passports. At this point, there is a good chance they will be returned.”
He continued: "There is not enough evidence to indict them so it is likely they will get their passports but I can’t guarantee it."
Asked if they can leave the country Mr Oliveira said: "None of the three have authorisation to leave the country at the moment. We don’t have the intention to keep their passports.”
Both men arrived at the station shortly after 1.30pm (5.30pm GMT) dressed in Team Ireland tracksuits.
Mr Kilty told reporters before arriving "we are here to cooperate" before entering the Cidade de Policia (Police City) in northern Rio.
Police were looking to speak with them about alleged ticket touting at the Rio Olympics.
Former OCI president Pat Hickey (71) has been detained at Gericino penitentiary - known locally as Bangu prison - in West Rio since last Friday.
He has been formally accused under Brazilian law of ticket touting, running a cartel and illicit marketing.
Mr Kilty and Mr Martin left the station shortly after 6.15pm (10.15pmGMT) with Mr Kilty telling reporters: "We are happy to have cooperated."
On Sunday police executed a warrant for the seizure of passports belonging to Mr Kilty and Mr Martin and that of their fellow board member Honorary General Secretary Dermot Henihan.
Warrants were also issued for the seizure of passports belonging to FAI chief executive and OCI vice president John Delaney, acting OCI president Willie O'Brien and personal assistant Linda O'Reilly. But they were not in Brazil at the time of the court order.
Officers were keen to ask Mr Kilty why he had 228 unused tickets in his room when they executed a warrant last Sunday.
Asked about this discovery Mr Oliveira said: "All the facts from today’s testimony will be checked out with other data and all of this will be passed to press at a press conference. They are focusing with the judiciary to verify the facts. Possibly pass to press afterwards
"They [Mr Kilty and Mr Martin] are witnesses. Neither of them were indicted.”
Speaking to the Irish Independent on Monday Mr Kilty denied having any knowledge of the alleged ticketing scam.
He revealed that the raid on Sunday was “as out of the blue for us as it was for anyone else”.
“I'm just absolutely shocked and amazed. This is unprecedented, it was the last thing I would ever have expected.
“We are here to cooperate. We will fully cooperate with the police, we have nothing to hide. We are here to do a job, we have always been here to do a job.
“All I can do is speak honestly and that's what I intend to do.”