Pat Hickey's family has called on the Foreign Affairs and Sports Ministers to "urgently intervene" to address some "extremely worrying" issues surrounding his arrest in Brazil.
Mr Hickey temporarily stepped down as the president of the Olympic Council of Ireland (OCI) following his arrest in Rio last week in connection with an investigation into alleged ticket touting.
In a statement, Anne Marie James, solicitor for Mr Hickey's family, says no charges have yet been brought, "nor has an appropriate venue for a bail application been made available".
The family is said to be concerned over a number of issues - such as the manner of his arrest, his detention without charge, and the effects of the arrest on his health.
They also highlight the "pre-trial disclosure of what is purported to be evidence to the media without any right of a reply", and are concerned his right to a fair hearing could be jeopardised.
They have requested an urgent meeting with Charlie Flanagan and Shane Ross, and hope to meet with the Taoiseach when he returns from holidays.
"The Hickey family is gravely concerned about the effect this degrading and humiliating ordeal has had on their Father and Grandfather and how it continues to affect his physical and mental health," the statement says.
"He has a serious heart condition and they are extremely anxious that he would be immediately released on bail and given the opportunity to respond to the accusations. They also, as a priority, want to get him home to Ireland as they have increasing concerns about his safety."
Separately, the OCI says it has appointed Grant Thornton to conduct an independent review into the ticketing arrangements for the Olympic Games.
The organisation says the review, when completed, will be given to Judge Carroll Moran, who is chairing the State inquiry into the matter.
Athletes will be invited to give evidence about their experience of ticket handling, and the inquiry will review areas such as the appointment of Pro10 Sports Management as OCI's authorised ticket reseller for the games.
It will also review interactions between Pro10 and THG (a separate ticketing company) in relation to OCI’s ticket allocation, and OCI’s interactions with THG.
The OCI says they hope the review will be concluded by October 10th.
The statement says: "As part of the Grant Thornton review, submissions will be invited from athletes and their families on their experience of ticketing allocation and availability arrangements for Rio 2016.
"The OCI is committed to a review of its wider corporate governance arrangements and will set out its intentions in this area in due course."
In response to the situation, the Minister for Foreign Affairs, Charlie Flanagan, has released a statement saying that his department are providing ongoing consular assistance to Mr. Hickey through the Irish Embassy and Consulate in Brazil.
“The Department cannot however provide legal advice or interfere in any way in the judicial processes in another country," he said.
Minister Flanagan has agreed to meet with the Hickey family and said that "arrangements will be made for this meeting to take place in the coming days. In the meantime, my Department is continuing to monitor developments in this consular case closely and is continuing to provide all appropriate consular advice and assistance to Mr. Hickey and his family.”