The central investigating agency has shown willingness to probe the murder provided it is assigned adequate man-power to work under CBI supervision during the investigation, sources said.
The CBI has made similar request to the Uttar Pradesh government in the National Rural Health Mission probe which was duly accorded by the state government.
The agency, which is facing an acute staff crunch, has been given the job of investigating into a large number of corruption and special crime cases spread across multiple locations making the probe an arduous task, the sources said.
Bihar Chief Minister Nitish Kumar had recommended a CBI probe into the killing of Ranvir Sena supremo Bramheshwar Singh shot dead on June 1.
A decision to this effect was taken during a meeting Kumar had with top state police and Home Department officials.
RJD supremo Lalu Prasad, LJP president Ram Vilash Paswan and Bihar Congress had also demanded a CBI inquiry to probe the killing.
The Ranvir Sena chief was shot dead by gunmen when he was taking a stroll near his house in Khopira village in Bhojpur district on June 1.