Last week, President Jonathan had asked a high level team to look into the possibility of granting the militants a pardon.
The announcement was made via an audio statement believed to be from the group's leader Abubakar Shekau.
According to the BBC, the group says its members are fighting to create an Islamic state in Nigeria's predominantly Muslim north.
Mr. Shekau said his group had done nothing wrong and so an amnesty would not be applicable to them.
It was the Nigerian government that was committing atrocities against Muslims, he said.
"Surprisingly, the Nigerian government is talking about granting us amnesty. What wrong have we done? On the contrary, it is we that should grant you pardon," AFP news agency quotes him as saying in the Hausa language audio recording.
The amnesty panel was set up by the President last week and it includes senior military representatives, presidential sources said.
The move surprised many as President Jonathan had dismissed the idea of amnesty and dialogue.
In recent years, Boko Haram has carried out a campaign of violence across northern and parts of central Nigeria killing at least 2,000 people.
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