Muhammadu Buhari has vowed to free the girls, whose abduction almost two and a half years ago from the northeastern village of Chibok triggered international campaigns and piled pressure on his predecessor Goodluck Jonathan.
Nigeria would "welcome intermediaries such as U.N. outfits, to step in", Buhari told U.N. Secretary General Ban Ki-moon on sidelines of the annual U.N. General Assembly in New York, a statement issued by the president's office said.
Buhari last year said for the first time his government was ready to negotiate over the girls. In August said he would let the Islamist militant group choose a non-profit organization as an intermediary but the group has not commented on the proposal.
Any negotiations would be the first publicly known talks between the government and Boko Haram, whose seven-year insurgency to create an Islamic state in the northeast has killed 15,000 people and displaced more than two million.
"The challenge is in getting credible and bona fide leadership of Boko Haram to discuss with," said Buhari.
Boko Haram pledged allegiance to Islamic State last year but signs of a rift emerged after IS announced a new leader for what it described as its West African operations. Boko Haram's hitherto leader Abubakar Shekau appeared to contradict the appointment in a later video message.
"The split in the insurgent group is not helping matters. Government had reached out, ready to negotiate, but it became difficult to identify credible leaders," said the president.
Nigeria's failure to find the kidnapped children prompted an outcry at home and abroad. Critics of Buhari's predecessor, Goodluck Jonathan, said his government was too slow to act.
Boko Haram published a video in August which apparently showed recent footage of dozens of the girls and stated that some had been killed in air strikes.
Authorities said in May that one of the missing girls had been found and the president vowed to rescue the others.
Nigeria is battling the jihadist group on the ground and with air strikes. A multi-national joint task force - comprising troops from Nigeria and neighboring Niger, Cameroon, Chad and Benin - is also fighting the militants.