But after a week of rising tensions following the men's sudden re-emergence in Ireland, it is clear that neither side yet knows how to resolve the issue.
A spokesman for the Government last night said it was clear the matter would "take time".
Colombia wants the three - Jim Monaghan, Martin McCauley and Niall Connolly - returned to the country to serve 17-year sentences for training FARC guerrillas.
But there is no clear legal avenue available to bring this about, as there is no extradition treaty between Ireland and Colombia.
Earlier this week, Tánaiste Mary Harney suggested the men could serve their sentences here instead, if Colombia signed up to a European convention on the transfer of prisoners. Several other South American countries are already party to the convention.
But legal experts have discounted that possibility on a number of grounds. One reason for scepticism is that Irish legislation to ratify some parts of the convention has yet to be passed, and the experts believe it could not be applied retrospectively to imprison the three here.
Nonetheless, it was one of the avenues raised at the Bogota meeting, which saw the ambassador to Mexico, Art Agnew, outline the Government's position to Colombian Vice-President Francisco Santos Calderon and Deputy Foreign Minister Camilo Reyes.
"Ireland will meet its obligations under international law," Mr Agnew said following the meeting.
The ambassador, who also handles diplomatic representation for Colombia, acknowledged that the lack of a treaty between the two countries presented "a problem", but insisted "there could be other mechanisms" that would permit the three men's extradition.
He said the two sides were looking into all the possibilities and that, ultimately, a ruling on extradition would be left up to the courts here.
Mr Santos said he was confident a solution to the "problematic" issue would be reached.