CBI spokesperson Kanchan Prasad said the closure report is likely to filed in the case this week.
The agency had reached conclusion to include names of Birla and Parakh in the FIR in connection with allocation of Talabira-II coal block after scrutinising related files during its nearly 16 month-long preliminary enquiry.
CBI sources said that allegations levelled by it in the FIR could not be substantiated by it.
The agency's decision to file the FIR in which it accused Birla and Parakh of criminal conspiracy and criminal misconduct on the part of government officials had come under criticism from the former Coal secretary who said in his book that "CBI is either outright incompetent or is playing a deeper game."
The FIR related to allocation of Talabira II and III coal blocks in 2005 and CBI had charged Birla, Parakh and other officials of Hindalco under various IPC sections including criminal conspiracy and criminal misconduct on the part of government officials.
In its FIR, the agency had alleged that during the 25th Screening Committee meeting, chaired by Parakh, applications of Hindalco and Indal Industries were rejected for mining in Talabira II and III "citing valid reasons".