Prime Minister Nawaz Sharif will make a decision on the new army chief on November 28 as the government does not want to disturb the authority of the current head, Rashid said.
The appointment of the new army chief is the right of the premier according to the Constitution, he told reporters.
Kayani has made it clear that he will not seek any further extensions and will retire on November 29. He was given an unprecedented three-year extension by the previous Pakistan People's Party-led government in 2010.
The Prime Minister has said he will announce the names of the new Chairman of the Joint Chiefs of Staff Committee and new army chief on the same day. Sharif has also said he will go by seniority.
The appointment of army chiefs has never been easy for civilian governments in Pakistan.
If the army has its way, the next head of the Joint Chiefs of Staff Committee will most likely be Lt Gen Haroon Aslam, currently the most senior general in the army, while naval chief Admiral Asif Sandila could bag the position if it goes to the navy.
Aslam served as Director General of Military Operations, commanded a division of the Special Services Group and headed the Bahawalpur-based XXXI Corps. He led an anti-Taliban drive in Swat Valley in 2009 and is due to retire on April 9.
If Aslam is made the new head of the Joint Chiefs of Staff Committee, Lt Gen Rashid Mehmood, Chief of General Staff, will become the army chief if the government goes by seniority.
Following Mehmood are Lt Gen Raheel Sharif, Lt Gen Tariq Khan, Commander of the Strike Corps at Mangla, and Inter-Services Intelligence (ISI) chief Lt Gen Zaheer-ul-Islam.
Kayani was appointed army chief by former military ruler Pervez Musharraf in late 2007.
Meanwhile, the Information Minister said the government had received reports about the Taliban refusing to hold talks with it only through the media.
"We will wait to see if the other side releases a clarification or makes some changes to their resolve," he said.
The banned Pakistan Taliban have ruled out talks after their former leader Hakimullah Mehsud was killed in a US drone strike on Friday. They have also vowed to launch a wave of revenge attacks.
Rashid said the proposed talks were between the government and the Taliban and a third party could not damage the process by conducting an attack.
"The drone attack cannot cause damage to the dialogue process," he claimed.
Asked about the fate of Pervez Musharraf after he was granted bail in the four major cases against him, Rashid said the former president was still on the Interior Ministry's Exit Control List and could not leave the country.
He said a case of high treason case against Musharraf was pending and investigations were underway.
"If we would have started proceedings against Mushararf immediately after being elected, everyone would have called it revenge," he said.