Foreign Minister Dermot Ahern is due to meet his Colombian counterpart in New York on Monday to discuss the situation.
A spokesperson for Mr Ahern said the Colombian minister had made the request as they would both be at the United Nations general assembly.
“He will explain that we have an independent judicial process and that the extradition application will have to go through this,” the spokesperson said.
Ireland does not have an extradition agreement with Colombia and legal sources believe that on the basis of the Appeals Court decision that found the three guilty, an Irish court would find it difficult to send them back.
The three - Niall Connolly, 38, from Dublin; Martin McCauley, 41, from Lurgan, Co Armagh, and James Monaghan, 58, from Donegal - were sentenced to 17 years in jail in June 2004 for training Marxist FARC guerrillas.
They were released on bail to appeal the decision but went missing, turning up in Dublin just after the IRA’s July announcement that it was standing down operations.