Michael Lynn's legal team claim that he may have tuberculosis, and have requested that the former lawyer be immediately transferred to hospital in Brazil.
According to his solicitors, Mr Lynn should be immediately removed from prison, and treated in hospital.
However, prison sources say the Mayo man is receiving in-house medical treatment.
Mr Lynn has been in prison in Recife, in the north-eastern Brazilian state of Pernambuco, since last August, as he awaits the conclusion of extradition proceedings, lodged by the Government.
Documents lodged to the Brazilian Supreme Court say Mr Lynn is suffering from "chronic intermittent asthma", and that a private physician believes his to be a possible case of pulmonary tuberculosis.
The defence team has requested that Mr Lynn be taken to the Royal Portuguese Hospital in Recife for tests and treatment.
They contend that the conditions for treatment within the Cotel remand prison, in Abreu & Lima, where Mr Lynn has spent the past nine months, are not adequate.
They say the director of Cotel has refused to allow a transfer to hospital without written consent from the Supreme Court.
Mr Lynn's lawyers claim that unless he undergoes laboratory testing and treatment outside of the prison his condition could worsen, due to an "environment with poor air circulation".
They further asserted to Supreme Court judge Marco Aurélio, who presides over the extradition case, that if Mr Lynn is not removed from prison, he could pose a risk of contagion to other prisoners remanded at Cotel.
Justice Aurélio requested an urgent report as to Mr Lynn's condition from the prison director, in a document dated 24 April.
However, a senior prison source said yesterday that medical staff at the hospital were not concerned about Mr Lynn's health, and do not consider his condition to be life-threatening.
"We have doctors here," he said. "It's nothing serious."
Acknowledging that Mr Lynn had requested a transfer to hospital, the supervisor said that if medical staff at the prison thought Mr Lynn warranted hospital treatment, he would be accompanied there by prison staff, and would remain in their custody.
"But, he's not that sick," he concluded, having conferred with medical staff. Mr Lynn is receiving medical treatment within Cotel prison.
Last February, Mr Lynn's attempted bail proceedings were knocked back by the Brazilian Supreme Court.
His defence team had claimed that the extradition documents lodged by the Government officials were lacking, and that his arrest warrant was not valid under Brazilian law.
He has been in Brazilian state custody since August 2013, when he was arrested while walking through a shopping arcade, in a small suburban area where he lived and worked as an English teacher, on foot of an international arrest warrant lodged by Interpol.
As with most prisons in Brazil, Cotel remand centre is over-crowded and holds many times more prisoners that it was built for.
Mr Lynn is housed on a separate pavilion within the prison, which is reserved for white-collar prisoners.