The terror sect is thought to have issued the demand during secret contacts with the government of President Muhammadu Buhari, who has said he is willing to negotiate for the girls' freedom.
Details of the new ransom request emerged ahead of the second anniversary of the girls kidnapping on the night of April 14, 2014, when they were abducted by Boko Haram gunmen posing as soldiers.
Despite their case receiving global attention because of the celebrity-backed #bringbackourgirls campaign on social media, diplomats and sources close to the negotiations say they are no closer to knowing the girls' whereabouts.
Yet in none of the raids have any rescued prisoners or captured fighters been able to give any convincing accounts of meeting or seeing any of the Chibok girls.
"I think they are probably in clusters rather than all in one place, but probably not far from each other," said Shehu Sani, a Nigerian senator and civil rights activist involved in peace attempts with Boko Haram. "Boko Haram knows they are a prized catch."
One source close to Boko Haram said that around three months ago, Boko Haram sent a message saying it would exchange the girls for a ransom of 10bn Naira, the equivalent of around £36m.
"The ransom demand has split the government," said the source. "Some think it would be worth it just to resolve the Chibok situation, but others say it will simply allow Boko Haram to hire yet more insurgent recruits."
The same source also said that a month after the ransom demand, Boko Haram had secretly passed the government a new video tape showing 15 of the kidnapped girls.
"The girls are asked what their Christian names are and what their new Muslim names are," he said, referring to the "conversion" that Boko Haram forces Christian prisoners to undergo. "They are also asked if they have been raped or mistreated, but they say no - they look relaxed."
Asked about the ransom demand, diplomats said only that they were aware of "rumours" of contacts of various sorts.
However, others involved in past attempts to free the girls claim that no proper "proof of life" video has ever been issued by Boko Haram, and dismiss talk of the group being interested in either ransom demands or prisoner swaps.
Among them is Dr Stephen Davis, an Australian clergyman and former Nigerian government advisor who spent four months in Nigeria in 2014 attempting to negotiate the girls' freedom.
He came close three times to negotiating the release of some of the Chibok schoolgirls, only for the group's high command to rule it out. "They realise that these girls are the ace in their hand," he said.
Instead, he claimed now says that the only way to get the girls back is to exploit the "combat fatigue" that is now growing on all sides of the conflict, be it the Boko Haram fighters, the combat-weary Nigerian army, or the terrified civilian population caught in the crossfire.
"Take away the footsoldiers, and you will also start getting information about where the girls are. Any other way is putting the cart before the horse."
Last week, Nigeria's Defence Headquarters launched "Operation Safe Corridor", a program to rehabilitate repentant Boko Haram fighters through camps where they will be offered jobs and training in return for undergoing biometric profiling.
The military said some 800 fighters had already signed up for the program, and that other camps would open across north-east Nigeria in coming months.
Dr Davis added that during his visits to Nigeria in 2014, a Boko Haram commander had once been passed him a grisly video showing what purported to be the human remains of some of the Chibok girls.
However, he had never passed it on because there was no proof that it was definitely them.
"There was nothing identifiable in the video, and without any proof that it was the girls, there was no way I was prepared to pass it to anguished relatives," he said. "On the other hand, I can't think of any other reason why the commander would have passed it to me."