Lawyers for Ba Odah, who was cleared for transfer in 2009, had tried unsuccessfully to win his release on health and humanitarian grounds, but Pentagon officials said he was receiving proper care.
Obama, who last month presented Congress with a blueprint for closing the prison, is seeking to make good on his long-time pledge before he leaves office in January.
But he faces stiff opposition from many Republican lawmakers, as well as some of his fellow Democrats.
The Pentagon has notified Congress of its latest planned transfers from among the 37 detainees already cleared to be sent to their homelands or other countries, an official said.
All members of that group are expected to leave by the summer.
Obama's plan for closing down the facility calls for bringing the several dozen remaining prisoners to maximum-security prison in the United States.
But U.S. law bars such transfers to the mainland, and Obama has not ruled out doing so by use of executive action.
'I do not have a timeline on when particular detainees will be transferred from Guantanamo,' Commander Gary Ross, a Defense Department spokesman, said in a statement.
'However, the administration is committed to reducing the detainee population and to closing the detention facility responsibly.'
Lawyers for Ba Odah, who was cleared for transfer in 2009, had tried unsuccessfully to win his release on health and humanitarian grounds, but Pentagon officials said he was receiving proper care.
The plan to resettle about a dozen inmates was first reported by the Washington Post. The U.S. official declined to name the countries ready to take them in.
Ten Yemeni men were sent to Oman in January, while others were recently sent to Ghana, Bosnia and Montenegro.
The Obama administration has ruled out sending Yemenis, who make up the bulk of the remaining prisoners, to their homeland because it is engulfed in civil war and has an active Al Qaeda branch.
Guantanamo prisoners were rounded up overseas when the United States became embroiled in wars in Iraq and Afghanistan following the September 11 attacks.
The facility, opened by Obama's predecessor George W. Bush, came to symbolize aggressive detention practices that opened the United States to accusations of torture.
