A search for her began on Sunday after a paper published an article about her alleged abduction, prompting a social media campaign demanding she be freed.
Her family say she was abducted from the south in August by a man who forced her to convert to Islam before marrying her in the northern city of Kano.
The man denies it was against her will.
The alleged abduction has ignited the debate about child brides and forced marriages in Nigeria.
The UN said more than one in three girls are married before the age of 18, mostly in poor rural families in Africa.
The family say they have made several efforts to bring Ese back from Kano, some 900km (600 miles) away from her home in southern Bayelsa state, but were told she was no longer their daughter.
There have been some 50,000 tweets using the hashtag #FreeEse since Sunday to put pressure on the authorities to rescue the girl.
The alleged abductor of the girl was a long-standing customer of Ese's mother, who is a food vendor, reports the BBC's Chris Ewokor from the capital, Abuja.
Prominent girls' rights activist and former World Bank Director Oby Ezekwesili and human rights campaigners have called for the prosecution of all those involved in the alleged kidnapping.
More on child marriage
There have been reports that the marriage took place at the palace of the Emir of Kano, Muhammadu Sanusi II, an influential Muslim leader in Nigeria.
But he has vehemently denied this.
The Emir said the girl was brought to his palace after her alleged conversion to Islam but he told the person to return her to her family because she was too young.
"We asked that if he really wants her he should wait for her until she turns 18 and then if she still wants him they can get married. No-one will stand in the way," Mr Sanusi said in a statement.
Meanwhile, Nigeria's Premium Times newspaper is reporting that the girl has said she wants to remain in Kano.
She told police she was not forced to convert to Islam, it reports.
In 2014, a 14-year-old girl used rat poison to kill a 35-year-old man she was forced to marry in the city.
A 13-year-old Nigerian girl who was allegedly abducted and forced into marriage has been found and will be re-united with her family, police say.