"They have been planning this exercise for months and have not changed the scenario to reflect current situations across the globe," according to Kageleiry.
President Obama has ordered the CIA to begin setting up distribution points in Jordan and Turkey, to start providing American arms to rebel forces.
That decision came after U.S. intelligence officials concluded the Assad regime had used chemical weapons against opposition forces.
American intelligence found Assad's forces had used chemical weapons, such as Sarin gas, against rebel positions in the northern part of the country on several occasions.
Assad's use of those weapons crossed a "red line" with the Obama administration, prompting the president to approve the arms supplies to Syria's rebels.
Aside from providing arms to Syrian rebels, the Pentagon has agreed to hand over American warplanes and anti-aircraft missiles to neighboring Jordan.
Along with the upcoming JOAX war game, U.S. forces are already "very involved" in providing non-lethal support to the rebels, and assisting countries like Jordan in preventing the war from spilling over Syria's borders, Defense Secretary Chuck Hagel said in May.
"Hundreds of DOD personnel are working alongside their Jordanian counterparts to enhance Jordan’s border security" and track the chemical weapons threat from Assad, Hagel said during a speech to the Washington Institute for Near East Policy.
In response, Kageleiry noted that "obviously Syria has chemical weapons" and the upcoming drills are focused on containment of those types of weapons.
However, she reiterated that there is no direct line between the exercises and any possible military action the United States may take in the region.
The main training scenarios in this year's JOAX drill are to conduct "an evacuation of American citizens along with reacting to intelligence indicating chemical weapons production and storage facilities," she said.
Along with the 82nd Airborne, members of the Army's 20th Support Command, Air Force Mobility Command as well as military representatives from France, Mexico and Italy will participate in the exercise, scheduled for next week at Ft. Bragg, N.C.