Special CBI Judge O P Saini put up the matter for October 8 after the counsel appearing for the agencies told the court that the main counsel was not well and requested time.
Advocates appearing for CBI and ED, K K Goel and Nitesh Rana, told the court that the agencies required time to file a detailed reply and argue on the application filed through Chidambaram's lawyer Arshdeep Singh.
Chidambaram and his son Karti were named in the chargesheet filed by the Central Bureau of Investigation in the case on July 19.
The agency filed a supplementary chargesheet before the special judge, who had fixed it for consideration on July 31.
The CBI is probing how Chidambaram, who was the Union finance minister in 2006, granted a Foreign Investment Promotion Board (FIPB) approval to a foreign firm, when only the Cabinet Committee on Economic Affairs (CCEA) was empowered to do it.
The senior Congress leader's role has come under the scanner of investigating agencies in the Rs 35-billion Aircel-Maxis deal and the INX Media case involving Rs 3.05 billion.
In its chargesheet filed earlier in the case against former telecom minister Dayanidhi Maran, his brother Kalanithi Maran and others, the agency had alleged that Chidambaram had granted an FIPB approval in March, 2006 to Mauritius-based Global Communication Services Holdings Ltd, a subsidiary of Maxis.
The Maran brothers and the other accused named in the CBI chargesheet were discharged by the special court, which had said the agency had failed to produce any material against them to proceed with the trial.
The Enforcement Directorate is also probing a separate money-laundering case in the Aircel-Maxis matter, in which Chidambaram and Karti have been questioned by the agency.
Both Chidambaram and Karti have denied the allegations levelled against them by the CBI and the ED.