The application was moved before a bench of Chief Justice G Rohini and Justice Jayant Nath who were hearing two pleas challenging the appointment process of the Delhi government.
Citing Transaction of Business Rules (TBR), the Delhi government said the LG should be directed to "reconsider his decision on the request of Council of Ministers of GNCTD".
The court has listed the application on November 25.
LG Najeeb Jung had on September 21 set aside Saini's appointment in March to the top post of Delhi Electricity Regulatory Commission (DERC), as it was done without taking his approval as mandated under the rules and procedure.
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The application said the high court, in its August 4 judgement interpreting the inter-relationship between the LG and the Council of Ministers, had said that if the LG does not agree with a decision taken by Council of Ministers, he was required to refer the matter to the President of India.
The government had appointed Saini in March after the
The first petition against the appointment was filed by Raman Suri, challenging Delhi government's December 2015 notification seeking applications for the post of DERC chairperson and one member.
Suri has argued that the chairperson of the commission should be a former high court judge, since the adjudication of disputes between generating companies or transmission licensees was a "judicial function".
His PIL also challenged Section 84 of the Electricity Act 2003, arguing that the provision that a judge "may" be appointed should be read as mandatory.
The second petition was filed by lawyer A Mishra seeking scrapping of the appointment by the AAP government as it was made without LG's approval.
The LG and AAP government have been at loggerheads over a range of issues, including appointments, and fighting it out in court.
The Delhi High Court had last month held that LG is the administrative head of Delhi which was a union territory, following which the AAP government had challenged the verdict in the Supreme Court.