Media reports Friday cited U.S. officials, whose names were not reported, as saying Bales, 38, was being flown to the United States from Kuwait. Citing his attorney, John Henry Browne, the Los Angeles Times reported Bales was being flown to a military detention center at Fort Leavenworth, Kan.
The U.S. military has not formally identified Bales publicly, CNN reported, citing military policy.
Afghan President Hamid Karzai told the families of people allegedly killed by the U.S. soldier he distrusts the U.S. military's version of what happened.
Karzai said the killing spree has pushed U.S.-Afghan relations to "the end of the rope," CNN reported. He said U.S. officials appeared to be withholding information.
Bales allegedly left an outpost in Kandahar province, Camp Belambay, and shot nine children, three women and four men in nearby villages Sunday.
"We tried to talk to the soldier involved, but there was no cooperation from America," Karzai told the families. "Based on what you are saying, the killer was not just one person."
Karzai said Afghan investigators are suspicious of U.S. video footage captured by security cameras, CNN said.
Bales has been described as a decorated veteran of three combat tours in Iraq. He was in his first deployment in Afghanistan. His unit was based at Joint Base Lewis-McChord in Washington.
He reportedly suffered a serious head injury in 2010 in a vehicle rollover in Iraq.
"I think it's of interest that we have a soldier who has an exemplary record, a decorated soldier who was injured in Iraq to his brain and to his body, and then despite that was sent back. I think that's an issue. I think it's a concern," said Browne, who told CNN he was representing Bales and had spoken with him by telephone.
A senior U.S. official told the Times Bales may have been drinking heavily just before the shootings, a violation of military regulations in combat areas.
"When it all comes out, it will be a combination of stress, alcohol and domestic issues -- he just snapped," said the official, who was briefed on the investigation and spoke on the condition of anonymity.
Browne, whose high-profile client list includes a teenage thief known as the "Barefoot Bandit," said a report of marital tension was "nonsense," the Times reported.
Bales and his wife, the parents of two children, had "a very healthy marriage," Browne said.