The OCI said it is a personal matter for Mr Hickey.
However, the OCI is currently paying Mr Hickey's legal fees.
A judge in Brazil ruled on Wednesday that the former OCI president is to be given back his passport.
Mr Hickey, 71, must pay a bond to the court of â‚¬410,000 (1.5m Brazilian dollars).
Justice Juliana Leal de Melo of the Special Court for Supporter and Large Events in Rio de Janeiro, which had jurisdiction during the Olympic and Paralympic Games, ruled that Mr Hickey can be allowed to leave Brazil "to treat a health problem".
The former OCI president is among ten people facing charges related to an investigation into alleged ticket touting at Rio 2016.
He has denied all allegations made against him.
Although he was released almost two weeks after his arrest in August, Brazilian officials retained Mr Hickey's passport.
Lawyers for Irish man Kevin Mallon, who has also been charged in this case and had his passport seized after his arrest in August, are expected to meet the relevant judge to reiterate a request for the return of Mr Mallon's passport.
There was no mention in the judge's decision on Mr Hickey on Wednesday night regarding the return of Mr Mallon's passport, but his legal team say this is not of concern to them.
Sao Paulo based lawyer, Franklin Gomes, said that the judge has not yet considered his plea to allow Mr Mallon to leave Brazil and that he will travel to Rio in the coming days to speak personally to the judge.
The Olympic Council of Ireland (OCI) has confirmed that it will not be paying the â‚¬410,000 bond which former president Pat Hickey has to pay as a condition of  being allowed to leave Brazil on medical grounds.