Three other executives have agreed to be questioned by police
A lawyer representing Pat Hickey has claimed that his arrest "has no legal support".
The president of the Olympic Council of Ireland (OCI) is facing charges relating to ticket touting at this year's Rio Games.
Mr Hickey had his passport confiscated and is currently being held at Bangu Prison following his arrest last week.
The 71-year-old was expected to appear in court today, but his case has reportedly been delayed due a backlog in hearings.
Mr Hickey's lawyer, Arthur Lavigne, said in a statement earlier: "Mr Hickey has been arrested due to suppositions that are not supported by any material evidence or proof of the alleged facts presented by the police.
"His arrest has no legal support.
"The investigation did not bring one single slight indication that Mr Hickey could be involved with the facts therein investigated, and his detention was required by the police authority under mere assumptions."
Meanwhile, three other OCI executives have agreed to be questioned by police in Brazil today, after their passports were taken during a search operation on Sunday.
Chef de Mission for the Olympics Kevin Kilty, OCI General Secretary Dermot Henihan and CEO Stephen Martin were forced to cancel their flights home and move to different hotels.
The head of the FAI, John Delaney, was back in work in Dublin yesterday despite a warrant issued in Brazil to seize his passport.