Muhammadu Buhari said that if a credible Boko Haram leadership could be identified then he was prepared to talk with them without preconditions.
But he said he had no intelligence on the girls' whereabouts or their health.
Boko Haram seized the girls from their dormitories in the north-eastern town of Chibok in April 2014.
"If a credible leader of Boko Haram can be established and they tell us where those girls are, we are prepared to negotiate with them, without any precondition," said Mr Buhari.
Attempts to negotiate with Boko Haram during the rule of ex-President Goodluck Jonathan failed because officials were talking to the wrong people in the fragmented militant group.
BBC Nigeria analyst Naziru Mikailu says Mr Buhari's offer to revive talks shows that Boko Haram remains a force, despite his claim last week that the group had been "technically" defeated.
There is little prospect of Boko Haram agreeing to negotiate the release of the girls, he adds.
The militants regard the girls as their most invaluable captives and their leader, Abubakar Shekau, said last year that most of them had converted to Islam and had been married off.
Some Nigerians on social media expressed anger at the president for saying the government had no idea where the girls were being held, saying it indicated a failure of the intelligence services.
Mr Buhari took office in May with a promise to defeat the group, and gave the military a deadline of the end of the year to end the six-year insurgency.
Although Boko Haram has been driven out from most of the areas it controlled in north-eastern Nigeria, it has continued to carry out suicide bombings and raids into neighbouring Cameroon, Chad and Niger.
The military has managed to free hundreds of Boko Haram captives in recent months.
However, they did not include any of the Chibok girls.
Using football to tackle Boko Haram
Why Boko Haram remains a threat

The midfielder, 20, agreed to a five-year deal with the French champions.
He scored 13 league goals for Anderlecht last season to help them win the Belgian title.
"Monaco is a club with an ambitious project, recognised on the European stage, and which relies on young players," Tielemans said.
"I am very happy to be here. I will now do everything possible to progress here and repay the confidence the club have shown in me."
Find all the latest football transfers on our dedicated page.

It said the scale of footpath erosion was "threatening Snowdonia's fragile nature".
The number of walkers climbing Snowdon has doubled since 2007 and more than four million people visited Snowdonia last year.
But the trust said grass species move in when pathways are eroded, strangling some plants.
Rhys Thomas, National Trust ranger for Snowdonia, said: "I've been building and rebuilding paths in the area for eight years.
"It's tiring, time-consuming and back-breaking work - involving hundreds of hours of volunteer time which requires shifting tonnes of stone by hand, vehicle and helicopter.
"But it's vital if we want to protect the delicate upland habitats that make Snowdonia a special place for wildlife."
Plants which could be at risk include purple saxifrage, moss campion and roseroot.
It is also home to the endangered Snowdon beetle - which in the UK are only found in Snowdonia.
The trust is trying to raise Â£250,000 to repair two-and-a-half miles of path.
It comes as concerns grow over the amount of litter being left on Snowdon, with some calling for a walker's charge to be introduced.
The appeal is supported by Hollywood actor Matthew Rhys, National Trust Wales's Snowdonia Ambassador.
Mr Rhys, who is from Cardiff, but has strong family connections to the national park, said he had seen the "trail of destruction left by the eroded paths" during visits to the area.
"There's a delicate balance to be struck between man and nature," he added.
National Trust Wales looks after almost 58,000 acres of mountain and farmland across the Snowdonia National Park.

Both Real and Atletico Madrid were banned after breaching rules over the transfer of foreign players under 18.
As part of the ban, football's world governing body Fifa said the young players involved were not allowed to play.
However, Cas has agreed to suspend that requirement while the appeal is heard.
Nigeria's president has said he is prepared to negotiate with Boko Haram militants to secure the release of about 200 schoolgirls.
[NEXT_CONCEPT]
Monaco have signed Belgium's young player of the year Youri Tielemans from Anderlecht for a reported 25m euros (£21.63m).
[NEXT_CONCEPT]
Snowdonia's pathways need to be preserved or plants and wildlife will be lost, National Trust Wales has said.
[NEXT_CONCEPT]
Real Madrid has told the Court of Arbitration for Sport (Cas) it will appeal against its Fifa ban on signing players.