The Nigerian government has denied that any deal was on the table and so far has neither confirmed nor denied the existence of the video.
Claims of the video's existence emerged as Air Marshal Alex Badeh, Nigeria's chief of defence staff, claimed that the military knew where the girls were located. Speaking late on Monday, he described it as "good news for the parents" but said that the military would not risk "going there with force".
Watch: Raw: Video claims to show missing Nigerian girls
He declined to give specific details, raising speculation about the accuracy of his claims. The Nigerian military has made several unsubstantiated statements in the past over the girls. Previous military attempts to free hostages have led to the prisoners being killed by their abductors, including two engineers, a Briton and an Italian, in Sokoto in March 2012.
The Nigerian journalist who is said to have obtained the latest video was named by the source as Ahmed Salkida, who is from the north-east state of Borno, Boko Haram's main stronghold. His contacts with the Islamists have been so close that in the past he has been arrested on suspicion of being a sympathiser. Two years ago, he moved with his family to Dubai.
The Nigerian government agreed for his return four weeks ago. He and a trusted cleric then risked their lives by heading into the remote bushland areas where the group operates, meeting a senior assistant of Abubakar Shekau, Boko Haram's leader.
"The government said to the intermediary to prove himself to show whether he was capable of brokering a deal or not, and insisted that he should obtain proof of life of the hostages," the source said. "So during his talks with the insurgents, he obtained a DVD which had clips of girls being interviewed by members of the group, in which they asked President Jonathan to do a prisoner swap.
A screengrab taken from a video of Nigerian Islamist extremist group Boko Haram claiming to show the missing schoolgirls. Photo / AFP
"That DVD was shown to the government, and a deal was arranged so that the girls would have been released a week ago on Monday, but at the last minute the government backed out."
The precise reasons for the government's alleged change of mind were not known, said the source. But he pointed out that the weekend before the proposed release date, Mr Jonathan was at a summit to discuss the Boko Haram crisis in Paris, also attended by British and American officials as well as the governments of Niger, Cameroon and Mali.
"The Nigerian government got a lot of offers of cooperation by neighbouring countries at the summit, and I think that emboldened them against negotiations," the source said. "They also seem to be afraid that if they do a prisoner swap, they will lose the support of the West."
As a result, the source said, the negotiations had now "crashed", with Mr Salkida returning to Dubai. The DVD remains in the possession of the Nigerian government and has not been released.