Official sources have revealed that the Home Ministry is currently examining the request for 40 companies, with 100 personnel each.
Bihar already has 2,400 paramilitary personnel in the state assisting the police in dealing with the Left Wing extremism.
A comprehensive plan is being worked out to launch a joint operation along the Bihar-Jharkhand border to flush out militants hiding there, sources added.
This comes in the wake of the hostage situation in the state where Maoists have abducted policemen to demand release of jailed rebels.
One of the four abducted policemen was killed earlier. The bullet-riddled body of kidnapped Bihar Military Police havildar Lucas Tete was recovered from Lakhisarai on Friday, Sep 3 morning.