The reports said government and Boko Haram representatives had held secret talks sponsored by the International Committee of the Red Cross (ICRC).
The deal would involve the release of the girls in exchange for 18 Boko Haram commanders held in prisons around the country.
Representatives of the two parties are now due to consult their leaders on the swap deal proposal, The Nation said.
Boko Haram kidnapped the girls from their school’s dormitory in the town of Chibok, in north-eastern Borno State, on 14 April. Some of the girls have since managed to escape from their captors.