The official, who spoke on condition of anonymity, said it was not yet clear if there was strong evidence linking the men to the death of Agent Nicholas Ivie, 30, earlier this week. Another agent was wounded in the attack.
Ivie and two other agents were fired upon after responding to a tripped sensor about five miles north of the Mexico/Arizona border. Ivie was a native of Provo, Utah, and worked for the Border Patrol for two years.
It was unclear if the agents were ambushed or if an actual gun battle occurred.
The other wounded agent was shot in the ankle and buttocks and was airlifted to a hospital with non-life threatening injuries. The third agent was unharmed.
An investigation into the shooting is being handled by the Federal Bureau of Investigation and the Cochise County Sheriff's Office.
The Associated Press contributed to this report.