Swamy appeared before the first bench comprising Chief Justice Sanjay Kishan Kaul and Justice Pushpa Sathyanarayana and sought urgent hearing of his plea.
"Today, tomorrow or at least next week," he pleaded and said he would take only five minutes to wind up his arguments if allowed on Tuesday itself.
Before the scheduled hearing date, procedural formalities such as filing of counter-affidavit by BCCI, rejoinders by others, if needed, and serving of copies on each other should all be completed, the judge said.
Earlier the bench had rejected pleas by the counsel for CSK Private Limited seeking early hearing of the PILs, ahead of the scheduled December 14 and 15.
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In his petition Swamy had submitted that the suspension of the "most popular and most successful" of all IPL teams was unfair.
Stating that the petition was filed in the interest of public and for the cause of cricket, Swamy had sought an interim stay order of Justice R.M.Lodha Committee banning CSK and Rajasthan Royals from IPL.