The apex court bench comprising Justices Dipak Misra and A M Khanwilkar asked the cricket board to file its reply within two weeks and posted the matter for further hearing on August 22 before the tender process concludes.
Swamy said that e-auction of the media rights should be done to ensure transparency, as it is to be given for the next five years.
Senior advocate Abhishek Manu Singhvi, appearing for Chief Eexecutive Officer (CEO) of the board, said that the tender process has been approved by the Vinod Rai, chairman of the apex court-appointed Committee of Administrators (COA).
"No, that judgement is altogether in a different background," the bench said, and asked the cricket board to file its reply within one week.
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It also asked senior advocate Parag Tripathi, appearing for (CoA) in the main BCCI matter pending before the court, to assist it in the case.
Singhvi said the e-auction process was not possible as the auction process has already started and will conclude next month. He said the court should not interfere with the process.
The apex court had earlier this month told the BJP leader that it would think over his plea for according urgent hearing in the case.
He had said that the amount involved in the award of IPL media rights was to the tune of Rs 30,000 crore and the issue should not be decided in an "opaque" manner.
"This petition prays that the distribution of IPL rights, which is scheduled on July 17, 2017 should be done in the most transparent mode available that is via E-Auction," his petition said.
It said that all the activities of Board of Cricket Control in India (BCCI) are undertaken with "tacit" concurrence of the state governments and the Centre "who are not only fully aware but supportive of the activities of the Board."
He alleged that there was a consistent attempt by vested interests to try and build a monopoly by getting the valuable rights in a non-transparent manner.
"Huge money is involved amounting to Rs 25000-30000 crore in the valuable rights associated with the game of cricket in India which makes it mandatory to have the auction process robust, completely transparent, in order to maximise revenue and prevent vested interests from making undue gains," Swamy said.
"No standard norms and objective criteria or procedures have been established for the distribution of the valuable rights associated with the game of cricket and selection or engagement of the rights holders.
"Lodha Committee has found that clear principles of transparency should be laid down, and BCCI's website and office should carry all rules, regulations and office orders of the BCCI in this regard, and there should be full transparency of all tenders floated and bids invited by or on behalf of the BCCI," it said.