A bench of Chief Justice G Rohini and Justice R S Endlaw also directed the central government counsel to take instructions by September 17 from the Ministry of Urban Development on the appointment.
The bench asked the counsel about the procedure to be followed for appointment of the Lokayukta.
"Take instructions from the government and we will take necessary action," the court said.
Delhi Lokayukta Justice Manmohan Sarin's five years tenure ended on June 5 last year.
The PIL filed through Kamran Siddiqui sought extension of Sarin's tenure as he had started inquiries in related cases and these were in the last stages when his tenure ended.