The matter was mentioned for urgent listing before a bench headed by Chief Justice Ranjan Gogoi.
Advocate Prashant Bhushan, appearing for petitioner NGO Common Cause and RTI activist Anjali Bhardwaj, appealed to the bench, also comprising Justices L N Rao and and S K Kaul, to hear the plea this Friday.
The CJI told Bhushan that it was "definitely not possible" to hear the matter on Friday and the plea would be heard next week.
CBI's Additional Director Rao was given the charge of interim chief on January 10 till the appointment of a new director after a high-powered committee headed by Prime Minister Narendra Modi removed Alok Kumar Verma as the chief of the probe agency on charges of corruption and dereliction of duty.
The petition has sought laying down of specific mechanisms to ensure transparency in the process of appointment of CBI director.
It has alleged that Rao's appointment was not made on the basis of recommendations of the high-powered selection committee, comprising prime minister, leader of the single largest opposition party and chief justice of India or a judge of the apex court nominated by him.
The plea stated that the order of October 23 last year appointing Rao as the interim CBI director was quashed by the top court on January 8 but the government has "acted in a completely mala fide, arbitrary and illegal manner" to appoint him again in "complete contravention" of the DSPE Act.
The plea has also sought a direction to the Centre to appoint a regular CBI director forthwith by following the procedure laid down in accordance with the provisions of the DSPE Act, as amended by the Lokpal and Lokayuktas Act, 2013.
Besides this, the petition has sought a direction to the government to ensure that "all records of deliberations and rational criteria related to short-listing and selection of the director, CBI, be properly recorded and made available to citizens in consonance with the provisions of the RTI Act".
The plea said that the government should ensure transparency in short-listing, election and appointment process of CBI director by publicly disclosing, including through the website, the procedure and rational criteria for short-listing candidates, if it is done.
The plea has sought a direction to the Centre that the process of selecting CBI director, including composition, mandate and minutes of the meetings of the search committee, should be disclosed publicly along with names of short-listed candidates so that people can inform the panel of any significant adverse information they may have about any such candidate.
The plea has claimed that lack of transparency in appointment of CBI director prevents any public scrutiny of the process and allows the "government to exercise undue influence" in the appointment process especially at the stage of short-listing of candidates.
Detailing the sequence of events relating to the appointment of Rao as the interim CBI director, the plea alleged that the entire process was "mala fide" as the government wanted to "appoint its own choice as CBI Director in the interim".
The apex court had on January 8 allowed Alok Kumar Verma to return as the CBI director, albeit with his wings clipped, by setting aside the Centre and the CVC's orders divesting him of his powers and sending him on leave.
However, the top court had said it was "still open" for the high-powered committee, which selects the CBI chief, to consider the matter within a week since the Central Vigilance Commission (CVC) was probing the charges of corruption against Verma.
It had set aside the October 23, 2018, orders of the CVC and the Department of Personnel and Training divesting Verma of his powers and asking Rao to look after the duties and functions of the agency's director.
On January 10, the high-powered committee removed Verma as the CBI Director. The same day, an order was issued by the government giving Rao the charge of interim CBI director.