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.
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.