The vast north-eastern Sambisa forest is where they have many bases - and it has been subject to aerial bombardments since February.
There has been speculation that some of the Chibok schoolgirls kidnapped more than a year ago are being held there.
Boko Haram has killed thousands in northern Nigeria since 2009.
Nigeria's military, backed by troops from neighbouring countries, launched an offensive against Boko Haram in February - and has recaptured most of the territory the militants had taken in the previous year.
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Some of the abducted schoolgirls, who escaped shortly after they were seized, have told the BBC they had been kept in militant camps in the Sambisa forest.
BBC Africa security correspondent Tomi Oladipo says the Nigerian military has been steadily reclaiming territory from the insurgents and sees the takeover of Sambisa as one of its biggest goals.
But our correspondent says the Sambisa forest, which incorporates a former game reserve, is far larger than any other territory that has been fought over so far.
The aerial bombardments on Sambisa, which is mainly in north-eastern Borno state, have been slowed down by weather conditions and poor visibility, he says.
Military spokesman Major-General Chris Olukolade refused to give any further details about the offensive.
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Outgoing President Goodluck Jonathan has been widely criticised for not doing enough to end the conflict.
But his government has now vowed to crush the group before he hands over to President-elect Muhammadu Buhari at the end of May.
An estimated three million people have been forced from their homes since 2009, when Boko Haram launched its insurgency to create an Islamic state.
Hundreds have also been kidnapped by the group, including more than 200 girls taken from their boarding school in the Borno town of Chibok last April.
Some of them who escaped shortly after the abduction told the BBC they had been kept in militant camps there.
Nigerian ground troops have joined an offensive on the last known hideout of the Boko Haram Islamist militants, a military spokesman has told the BBC.