Aziz's attorney Badia Aref said he had been getting more access to Aziz from US authorities in the last few weeks, and that legal developments he was not able to disclose had made him expect Aziz would be released soon.
Aziz is jailed along with Saddam Hussein and other senior members of the Baath Party overthrown after the US invasion of Iraq in April 2003.
"I expect he will be set free soon, but not within days," attorney Aref, who last saw Aziz on Tuesday during a visit to the US run facility near Baghdad, said.
"There are several legal elements that have emerged from the interrogations that have made me form an almost complete conviction that Aziz would be freed soon," Aref said.
No charges have yet been brought publicly against Aziz, who Aref said had been questioned by the US military exhaustively in 152 sessions.
"Maybe the interrogations have come to an end. I don't know," Aref said. He added he had turned down a US offer of accommodation near the detention centre.
"Because of the difficulties I am encountering in my movements to the detention centre, the Americans offered me a place to sleep. I turned down the offer to be in a camp that is set up in country ... they are occupying," Aref said.
Aziz, an Iraqi Christian, was the face of Saddam's government in foreign capitals and at the United Nations.
Aziz was the face of Saddam's
government in foreign capitals
Aref denied that Aziz, who was number 25 on the US military's list of the 55 most-wanted Iraqis in the aftermath of the invasion, might turn a star witness for the prosecution and testify against Saddam.
So far, Saddam has been formally charged in only one case - the alleged killing of Shias in the village of Dujail following a failed assassination attempt in 1982. A date for that trial is expected to be set soon.
Aziz was expected to get his first visit from his family in the next two days, only a week after the former senior official took a 10-minute phone call from them after waiting for over two years, Aref said.
"In the next two days he will be visited by his family including his grandchildren and daughter," Aref said.
Aref said Aziz, who is in his late sixties, was exhausted physically and was in ill health.
"He is exhausted and would die in prison if he stays in captivity another year," Aref said.
He also said his client might be released shortly but did not give any details about the subject and added that the Americans had many reservations the manner in which Iraqi investigators were questioning the accused.
Aref mentioned that his client was detained without any charge adding that Aziz is willing to appear before a court provided he was informed as to who the judges would be, before hand.