Sources said a panel of three senior IPS officials is likely to be formed during the meeting and the names will be put before the Appointments Committee of Cabinet headed by Prime Minister Manmohan Singh.
CBI Director A P Singh is due to retire on November 30.
Both Singh, Kumar and senior officials from Department of Personnel and Training (DoPT) had earlier met on October 18 but the names could not be finalised.
The names which were being considered are Ranjit Sinha, a 1974-batch IPS officer of Bihar cadre, S C Sinha (Haryana:1975), Neeraj Kumar (AGMUT:1976) and V K Gupta (Gujarat:1977).
While Ranjit Sinha heads the Indo Tibetan Border Police force, S C Sinha is at present Director General of National Investigation Agency. Kumar is Delhi Police Commissioner and Gupta is working as Special Director at CBI headquarters in Delhi.
A P Singh took over the reins of the CBI in November 2010 for a fixed period of two years. During his tenure, CBI handled high-profile corruption cases, including 2G spectrum, Commonwealth Games and coal blocks allocation scam among others.