General Abizaid declined to give an exact number of potential troop cuts.
Administration officials who spoke on condition of anonymity said planning for more substantial troop cuts was preliminary.
The panel has proposed a total troop cut of 100,000, with 50,000 of the troops to come from Europe.
The Administration's January budget proposed a total troop cut of 38,000.
Labour said the announcement would mean regular troop cuts of 19,000.
But he insisted that any troop cuts must not be perceived as a reaction to American casualties.
Pentagon planners have said troop cuts will not represent a retreat from American responsibilities.
In any case, Seoul will try to bargain for smaller troop cuts.
The troop cuts could number in the tens of thousands and would help pay for a new generation of weapons.
Efforts to cut the United States budget are also creating pressure for deeper troop cuts.