Bergdahl spent five years in captivity until his release May 31, in exchange for five Taliban figures being held at a U.S. military detention facility in Guantanamo Bay, Cuba.
Bergdahl, 28, returned to the United States -- specifically to an Army medical facility in San Antonio, Texas -- early Friday.
The investigating officer looking into the circumstances surrounding how Bergdahl went missing is expected to begin working on the case next week, though that doesn't necessarily signal anything about when the sergeant will undergo formal questioning.
The senior defense official declined to name the general who will investigate until there is a formal announcement.
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.
The Army has no definitive finding that Bergdahl deserted because that would require knowing his intent -- something officials couldn't learn without talking to the soldier, a U.S. military official recently told CNN.
Bergdahl arrived in San Antonio from a military hospital in Landstuhl, Germany, where he'd been recuperating since his release May 31 in exchange for five Taliban figures held at Guantanamo Bay, Cuba. Officials have described Bergdahl's condition as stable.
With Qatar as the broker, the United States struck a deal with the Taliban to free Bergdahl.
The Obama administration didn't tell Congress of the releases. Under law, the White House has to give a 30-day notice to Capitol Hill before any terrorists are transferred from Guantanamo.
Believing that his health was deteriorating, the administration said it acted quickly to save his life.
U.S. special operations forces recovered Bergdahl without incident on May 31 at a helicopter pickup point in eastern Afghanistan, near the border with Pakistan.