The official wanted to remain anonymous and the government has not issued a statement.
Previous reports of the girls’ release have turned out to be wrong.
The Islamist militant group kidnapped more than 270 students from a school in Chibok in April 2014 – an act that provoked international condemnation.
It also sparked one of the biggest global social media campaigns, with tweeters using the hashtag #BringBackOurGirls.
The BBC’s Martin Patience in Nigeria says the government official did not say how the kidnapped students had been rescued.
But the military is currently carrying out a large-scale operation in the Sambisa forest, which is a Boko Haram stronghold.
There has only been one confirmed release of a student kidnapped from Chibok more than two years ago.
In May, a 19-year-old woman was found carrying by an army-backed vigilante group.
After that it was believed that 218 students were still missing – more than 50 managed to escape on the day they were captured.
Boko Haram has also kidnapped thousands of other people during its seven-year insurgency in north-east Nigeria.