Geelani died here on Thursday evening following a cardiac arrest at the Fortis Hospital where he was admitted for breathing and other problems.
Sources in the Delhi Police told that the decision to conduct the post-mortem at AIIMS was taken in view of the fact that Geelani was their protectee.
And by doing so, the sources said that police wanted to keep everything on record in case any controversial situation emerges in the future.
"Initial investigations have revealed that he died of heart failure," they added.
In 2001, Geelani was arrested by the Delhi Police in connection with the Parliament attack case but acquitted for "lack of evidence" by the Delhi High Court in October 2003, a decision upheld by the Supreme Court in August 2005, which at the same time had observed that the needle of suspicion pointed towards him.
In 2005, he was shot at when he had gone to meet his lawyer and was admitted to AIIMS. After this incident, he was provided security by the Delhi Police.
In February 2016, Geelani was also arrested on sedition and other charges in connection with an event in New Delhi in which anti-India slogans were raised.
He is survived by his wife and two daughters. He used to teach Arabic language at Delhi University's Zakir Hussain College.
He was living with his family in Delhi's Zakir Nagar. It was reported that the family intends to take the body to Kashmir after the post-mortem, but Delhi Police is yet to confirmn this.
Security has been beefed up at AIIMS and in Zakir Nagar where many people assembled to meet the bereaved family.
( With inputs from IANS )