His lawyer is in discussions with the Department of Foreign Affairs and the Department of Justice, with a view to obtaining permission for Mr Jabbarov to stay here.
If the Government agrees, it will be the first time an EU country has taken in a foreign national Guantanamo inmate.
Mr Jabbarov was captured by US troops in 2001 in Afghanistan, where he had been living as a refugee. He has been at the Cuban detention centre since 2002 and has been cleared for release since early 2007.
His Boston-based lawyer, Michael Mone, has discussed his client's predicament with officials from both relevant Government departments.
"I think he would be a perfect fit for Ireland," Mr Mone said. "He has told me over and over again that he wants to be settled in a country that is free, safe and democratic."
Mr Jabbarov is one of around 30 detainees who have been labelled "Guantanamo's refugees". These are inmates who have been cleared for release by the US government yet remain imprisoned at Guantanamo because they come from "high-risk" countries where there is a potential danger of persecution or torture should they be forcibly returned.
So far, no country, other than Albania, has been willing to accept these refugees from Guantanamo for resettlement.
Mr Mone has alleged that his client had a "chilling encounter" with Uzbek officials who came to Guantanamo in September 2002 to interrogate him.
"The Uzbek interrogators told Oybek he would be sent to prison upon his return to Uzbekistan and implied he might face torture to force him to confess to things he did not know," Mr Mone said.
Barack Obama's victory in the US presidential election earlier this month has brought increased calls for the closure of Guantanamo.
Mr Obama has indicated he will treat the matter as a priority in the early stages of his administration.
Amnesty International has urged the Irish Government to take in one or more of the detainees, arguing that it would be leading by example if it became the first EU state to do so.
The proposal is believed to have met with resistance within the Department of Justice.
However, some in the Department of Foreign Affairs believe the Government could win favour with the Obama administration by agreeing to resettle at least one detainee.