The agency wanted to examine him in connection with a Foreign Investment Promotion Board (FIPB) clearance given to media group INX Media for receiving funds from Mauritius when his father P Chidambaram was the finance minister.
It is alleged that a firm "indirectly controlled" by him received money from INX Media, run by Indrani and Peter Mukerjea.
The sources said the agency had issued notices to Karti, 45, and his associates to appear for questioning between June 27 and June 29, but they failed to turn up.
The CBI had registered the case on May 15 against Karti, his company Chess Management Services, INX Media, Advantage Strategic Consulting Services, its director Padma Vishwanathan and the Mukerjeas. The Mukerjeas, charged with the murder of Indrani's daughter, Sheena Bora, are currently in jail.
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The agency had raided 17 locations, including the Chidambarams' residence in Chennai.
According to the CBI, INX Media stated in its records that an amount of Rs 10 lakh was given to Advantage Strategic Consulting (P) Limited, a firm the CBI said was "indirectly" owned by Karti, for management consultancy charges towards an FIPB notification and clarification.
The CBI alleged that Karti received the money from INX Media for using his influence to manipulate a tax probe against it in an FIPB violation case for an investment from Mauritius.
His father had issued a strong statement in response to the FIR, saying that the government was using the CBI and other agencies to target his son.
FIPB approval was granted in "hundreds of cases", the senior Congress leader had said.