Adamu was expected to be out of office from today on retirement.
There are speculations about the appointment of AIG Zanna Ibrahim as the new IGP. The presidency is yet to confirm or refute.
The presidential aircraft landed this evening at the Nnamdi Azikiwe International Airport Abuja.
Buhari was on a four-day official visit to his hometown in Katsina State.
The Nigerian leader was also received by Chief of Staff, Ibrahim Gambari, Minister of the Federal Capital Territory, Muhammed Bello, among others.
Buhari participated in the All Progressives Congress (APC) membership registration and revalidation exercise at the Sarkin Yara ward on Saturday.The Inspector-General of Police, Muhammed Adamu welcomed President Muhammadu Buhari back to Abuja on Tuesday.
The President was sighted with not wearing face masks of the COVID-19 law.
He later hosted some APC governors who accompanied him to the venue of the registration exercise