The Government has put forward a plan to the Colombian authorities that could lead to the Colombia Three being released quickly from jail in Bogota and deported.
The outline of the Government's proposals was offered by the Taoiseach, Mr Ahern, during "a very positive" meeting with the Colombian President, Mr Alvaro Uribe, on Saturday in Mexico.
A Colombian judge last month acquitted Mr Niall Connolly, Mr James Monaghan and Mr Martin McCauley on charges of training Marxist FARC rebels, though they were jailed for carrying false Irish passports. The Colombian Attorney General's office lodged an immediate appeal against the verdict.
The Government has now proposed that the decision to appeal be reviewed, which leaves open the possibility that a more senior legal officer could decide not to go ahead with it.
The Taoiseach also suggested on Saturday that the men could be released and sent back to Ireland, and then required to honour bail conditions and report frequently to gardaí.
The Minister for Foreign Affairs, Mr Cowen, and the Secretary General of the Department of Foreign Affairs, Mr Dermot Gallagher, told Colombian officials that "a regime could be put in place" to deal with the men if they were sent back to Ireland.
Colombia Three supporters have urged the Taoiseach to "keep up the pressure" on President Uribe, though they acknowledged that Saturday's talks were "very significant".
Promising to report back to the Taoiseach within 10 days, Mr Uribe said he would discuss with legal and constitutional authorities in Colombia how the legal process could be speeded up.
The leading campaigner on behalf of the trio, Sinn Féin's South Down Assembly member, Ms Caitriona Ruane, said she had spoken to the men's families: "They are delighted that the Taoiseach and President Uribe have met.
"It is a very significant meeting and something we have been asking the Irish Government to seek for some time. President Uribe is a very powerful man in Colombia.
"I think what is clear to everybody, including the Irish Government, is that these men need to be brought home and I hope this meeting goes a long way to getting them back swiftly," she said.
Ms Ruane spent over three weeks in Colombia last month dealing with the men's case: "We had to move hotels five times because of the danger," she told The Irish Times.
Meanwhile, the Colombian president has embarked on an effort to isolate the FARC by offering to hold peace negotiations with a smaller rebel group, the National Liberation Army, even if it does not stop fighting.
The men's situation was discussed in Dublin last Monday by the Taoiseach and Mr Cowen, and Ms Ruane, who has repeatedly claimed since the men's arrest in 2001 that they faced death.
