Justice Pratibha M Singh directed that the petition filed by advocate Chaitanya Rohilla be listed before another single judge bench subject to the orders of the Chief Justice.
"Let the matter be treated as a Public Interest Litigation (PIL)," the bench suggested.
The plea will now be listed before another bench and would come up for hearing on 18 January.
The petition states that the policy gives a 360-degree profile view into a person's online activity and that this level of insight into a person's private and personal activities is done without any government oversight.
During the course of the hearing, Advocate Manohar Lal appeared for the petitioner, the Centre was represented by Additional Solicitor General (ASG) Chetan Sharma, and senior advocate Mukul Rohatgi appeared for WhatsApp.
Rohilla has also sought direction from the Ministry of Electronics and Information Technology to lay down guidelines to ensure that WhatsApp does not share any data of its users with any third party or Facebook and its companies for any purpose.
The petitioner has further submitted that the sharing of users' data by WhatsApp to third parties and Facebook is in itself illegal because the messaging platform can only use the information for purposes that are reasonably linked to the purpose for which the information was given.
It ruled that the absence of a data protection authority leaves the users with a company's own assurances and privacy policies.
The petitioner also pointed out that India, being a signatory to the International Covenant on Civil and Political Rights (ICCPR), is obligated to implement essential data protection regime in both the public and private sectors.
WhatsApp is asking users to either give their consent to sharing data with Facebook or lose their accounts after 8 February. To continue using the services, users will have to accept the terms and conditions.
If the users do not accept the new terms of service, they will no longer be able to use the app.