Relatives of the victim told newsmen that she was last seen while leaving her elder sister's house at Dideolu Estate in the Oniru area of the state in the evening of Friday last week.
When our correspondent visited the victim's home on Wednesday, family and friends thronged the place to commiserate with her mother.
A relative of the victim, who craved anonymity, said Ayobami left her two phones and handbag behind in the house at the time of her kidnap.
He said the matter was initially reported as a case of missing person.
He said, "On Friday, she suddenly left the house and walked outside the main gate of the estate. We have not heard anything from her since then. Her phones were here so there was little we could do.
"We asked the security guards at the gate if they noticed anything, but they said they only saw her walking out and no vehicle was seen nearby.
"We reported the matter to the Maroko Police Division, as well as the state command headquarters."
It was learnt that following her disappearance, friends of the victim began sending messages on smartphones and the social media, begging members of the public to help search and provide details regarding Ayobami's whereabouts.
It was however learnt that on Wednesday afternoon, a man, who refused to identify himself, called the victim's elder sister on the telephone, demanding N10m as ransom.
The relative said, "We did not speak with Ayobami, but someone called with a private number demanding N10m.
"When we tried to ask further questions about the state of our daughter, the man terminated the call abruptly."
Our correspondent learnt that Ayobami's place of NYSC primary assignment is the Lagos State Ministry of Works, Alausa, Ikeja.
The victim, who graduated from the University of Maryland in the United States, was said to have returned to the country in January for her youth service.
Some of her colleagues, who visited the family home on Wednesday, described her as a hardworking and responsible lady.
One of them, who identified himself simply as Gbade, said, "Ayobami serves in the same ministry as me. We are also part of the same Community Development Service known as Education and Enlightenment.
"We are here to show support and we believe that by God's grace, she will return safely to her family."
The victim's brother-in-law, Mr Bosun Ayinde, confirmed to our correspondent that kidnappers had contacted the family.
"We want Ayobami back safe and sound. We have not rested since she left and you can imagine what her mother is going through," he said.
Police Public Relations Officer, Ngozi Braide, said the police had commenced investigation into the matter.