The cases relate to alleged irregularities in grant of Foreign Investment Promotion Board (FIPB) approval to the Aircel-Maxis deal.
Chidambaram and Karti were named in the charge sheet filed by the CBI on July 19 last year.
The CBI is probing how Chidambaram, as finance minister in 2006, granted FIPB approval to a foreign firm, when only the Cabinet Committee on Economic Affairs (CCEA) was empowered to do it.
The ED is also probing a separate money-laundering case in the Aircel-Maxis matter, in which the Chidambarams have been questioned by the agency and their anticipatory bail is pending.
The Chidambarams have come under the scanner of investigating agencies in the Rs 3,500-crore Aircel-Maxis deal and the INX Media case involving Rs 305 crore.
It was during his tenure as finance minister in the UPA-I government that clearances from FIPB were given to the two ventures.
In the INX Media case, the CBI had registered an FIR on May 15, 2017, alleging irregularities in the FIPB clearance granted to the media group for receiving overseas funds of Rs 305 crore in 2007 during Chidambaram's tenure as finance minister.
Thereafter, the ED in 2018 lodged the money-laundering case in this regard.
Apart from them, Chidambaram's wife Nalini has been chargesheeted by the CBI in the Saradha chit-fund scam for allegedly accepting a bribe of Rs 1.4 crore.
The Calcutta High Court in February this year granted her interim protection from arrest in the case.
Chidambaram was recently asked by the ED to join the investigation relating to Air India purchase probe in which his former cabinet colleague, Praful Patel, also faced questioning from the probe agency.
Besides that, the Madras High Court had in November last year quashed the sanction orders issued by the Income-Tax department to prosecute Chidambaram, Nalini, son Karti and daughter-in-law Srinidhi Karti Chidambaram under the Black Money (Undisclosed Foreign Income and Assets) and Imposition of Tax Act, 2015.
The high court order has been challenged in the Supreme Court where it is pending.
CBI has initiated a preliminary enquiry into allegations that a hotel in Tamil Nadu was grabbed by a relative of the former finance minister in collusion with officials of Indian Overseas Bank (IOB).
A complaint is also pending with Delhi Police relating to the alleged manipulation of an affidavit in connection with the Ishrat Jahan case.
The controversy regarding the affidavit assumes importance as Chidambaram was then the Union Home Minister.