(CNN) -

Army Sgt. Bowe Bergdahl is "just about done" with the final phase of his reintegration, a military source with access to information on Bergdahl's care told CNN.

He is expected to be assigned shortly to a new Army unit, the official said. Any issue of leave would be up to that unit.

Bergdahl, the U.S. soldier held captive for five years by militants before his release in May, has ventured several times off an Army base in Texas as part of the effort to get him used to everyday life in America, a military spokeswoman has said.

His release on May 31 in exchange for five Taliban being held by the U.S. military has rankled some, including former members of his unit, who said he was a deserter who endangered colleagues searching for him.

Yet while investigating circumstances surrounding his departure, the military has also said it's focused on making sure Bergdahl gets better mentally and physically, so he can gradually readjust to normal life.

Since being freed, Bergdahl has been carefully monitored at a military hospital in Landstuhl, Germany, and at his military home since June 13, Joint Base San Antonio-Fort Sam Houston.

He recently transitioned from inpatient care at Brooke Army Medical Center in Texas to outpatient care, the Army said on June 22.

Still, Bergdahl has hardly left the care of military health professionals.

Members of his reintegration team escort him whenever he leaves base and interacts with the public, the Army spokeswoman said. His stops have included restaurants, a library, a supermarket and several stores of his choosing.

Bergdahl went missing on June 30, 2009, in Afghanistan's Paktika province, where he was deployed with the 1st Battalion, 501st Infantry Regiment, 4th Brigade Combat Team, 25th Infantry Division.

An Army fact-finding investigation conducted in the months after his disappearance concluded he left his outpost deliberately and of his own free will, according to an official who was briefed on the report.

But there was no definitive conclusion Bergdahl was a deserter because that would require knowing his intent, something officials couldn't learn without talking to him, a U.S. military official has said.