The rebels are seeking the release of eight jailed Maoist commanders in exchange for the policemen.
The Janadalat or kangaroo court of the Maoists will meet any time after 11 am to decide on the fate of the policemen, kidnapped after Sunday's encounter with Maoists in Lakhisarai district.
Maoists have refused to give any more extension after the second deadline expired at 10 am on Thursday.
A massive search continued for the fourth consecutive day on Thursday to trace the four policemen.
The Bihar Police has said that it had vital clues about where the securitymen were being kept.
Inspector-General (Operations) K S Dwivedi, told PTI from Lakhisarai that the combined forces of CRPF, SAP, BMP and Special Task Force of the Bihar police were continuing with their search.
"We have specific information about where the securitymen are kept in captivity in the hills covering the districts of Munger, Jamui and Lakhisarai," Dwivedi said, adding a lot of people were cooperating in the drive against the Maoists.
Despite indication by Bihar government that it might consider holding talks with the ultras for securing release of the policemen, no official response from the ultras reached the state police headquarters, official sources said.
"We may think of holding talks, but with whom at this stage? Should we talk to people in the air? They (Maoists) have not officially approached us as yet on any demand," DGP Neelmani had said on Wednesday.
Official sources said Chief Minister Nitish Kumar was also monitoring the progress of the operation with the CRPF using helicopters to search for the policemen.
Avinash, a self-proclaimed Maoist spokesman, had in a communication to the chief minister's official residence in Patna conveyed the deadline of 4 pm yesterday for release of the eight Maoists, failing which, he said, the four policemen would be killed.
The Maoists had kidnapped sub-inspectors Rupesh Kumar and Abhay Prasad Yadav, BMP havildar Ehtesham Khan and BMP ASI Lucas Tete after the encounter.
Six Bihar Military Police personnel, officer-in-charge of Kawaiya police outpost Bhulan Yadav and a policeman were killed in the gunfight with Maoists in the Kajra police station area.
Meanwhile, the families of the kidnapped policemen have appealed to the state govt to give in to Maoists demands to guarantee the safety of their loved ones.
Captured cop, Abhay Yadav's wife Rajni Devi on Wednesday met Nitish and was assured of her husband's safe return.
Speaking to media persons, Lucas Tete's wife Pyari added, "I urge the Maoists to release my husband. How will we survive if he is killed?"
Eshaan Khan's wife said, "My husband was kidnapped during an ambush. I request the government to please bring him back safe."
A bereft Rupesh Kumar's mother also made an emotional appeal to the government for the safe return of her son. "We haven't heard from our son at all. The Maoists have asked the government to fulfil their demands or else our son will be killed," she said.