"That is the offer to him. But we dont know yet his decision," Executive Secretary Eduardo Ermita said.
Ermita did not elaborate on the matter but mentioned that Abu was a classmate of Indonesian President Susilo Bambang Yudhoyono at Fort Leavenworth in Kansas in 1991.
In earlier reports, Abu said he and the Indonesian leader had been good friends. "We are (still) communicating with each other," he said.
Abus experience in diplomacy includes being the defense attaché of the Philippine Embassy to the Court of St. James in the United Kingdom. He finished his masters degree in war studies in London.
Abu will formally bow out of the military service on Monday and be replaced by Lt. Gen. Generoso Senga, commanding general of the Philippine Army.
Abu was supposed to have left on June 24 upon reaching the mandatory retirement age of 56 but President Arroyo extended his tour of duty because of destabilization threats against her administration.
The President is facing ouster calls from the opposition and other groups due to alleged election fraud and corruption.
Abu is said to be one of Mrs. Arroyos most trusted men. He was the commanding general of the troops that crushed the mutiny staged by some 300 junior officers and servicemen on July 27, 2003 in Makati City.
Abu was also the chief of Task Force Libra, which in 2001 quelled an attempted takeover of Malacañang by thousands of supporters of deposed President Joseph Estrada.
Mrs. Arroyo appointed Abu amid the corruption scandal rocking the military leadership in October of last year.
The decorated Abu is a graduate of Philippine Military Academy (PMA), class of 1972. He also took advanced courses in military science at Fort Leavenworth and Fort Benning in the United States.
He has a masters degree in business administration from the University of the Philippines and a masters degree in war studies from the Kings College, University of London, Britain.
Abu also finished portfolio management from the Financial Executive Institute of the Philippines.
Maj. Gen. Hermogenes Esperon Jr., the commanding general of the Special Operations Command, meanwhile, will take over the Philippine Army.
Esperon, on the other hand, is currently the general of the Special Operations Command, the first national maneuver force of the AFP which includes the elite First Scout Ranger Regiment, the Special Forces Regiment and the Light Reaction Battalion.