Prime Minister Narendra Modi heads the committee, in which the Chief Justice of India and the Leader of Congress in Lok Sabha Mallikarjun Kharge are the other members.
The sources said the government had proposed the meeting on January 21 earlier while Kharge wanted the meeting on January 24 or 25.
After mutual consultations, the government has finalised January 24 as the date for the meeting to select the new CBI Director, a post which is lying vacant ever since the government removed Alok Verma and appointed him as Director General Fire Service.
IPS officer M Nageswara Rao was named the interim director of the CBI.
The Congress has been attacking the prime minister for not appointing a regular CBI Director.
Kharge had also written to the prime minister demanding early holding of the meeting of the high powered committee to appoint a regular CBI Director.