"She decided when the time was right and she swooped down and took him when she saw the time was right and she saw an opportune moment," Miller said.
Nelson has a criminal history that includes charges of aggravated robbery, drug charges and threatening a woman.
A next door neighbor of Jonathan's mother, Angela Davis, told KTRK that Nelson was with the family when they were looking for the missing boy on Christmas Eve.
"She [Nelson] was just sitting there, looking at what was going on," Rita Jackson told KTRK.
Houston Police wouldn't comment on the neighbor's claims.
Smith described Nelson as an "acquaintance" of Jonathan's family. "She knew [Jonathan's] mother's roommate and she was a former maintenance worker at the apartment complex," Smith said.
Nelson is also believed to be the woman who Jonathan's mother claims answered the phone at her home on Christmas Eve, a chilling call that had authorities concerned for Foster's safety.
Smith said that Houston police are still investigating the phone call.
Mary Gifford, the boy's grandmother, said that when her daughter called her son on Friday, a woman she did not know picked up the phone.
"My daughter asked to speak with her son, and then the woman asked [Jonathan] if Angela was his mother," said Gifford. "He said, 'Yes ma'am, Angela is my mother,' and then the phone went dead."
Gifford, who had been holding out hope that her grandson would be found alive, told ABCNews.com earlier this week that she's devastated over his death.
"I'm trying to hang in there, but what would be going through your mind if this happened to your child?" she said. "I keep thinking 'Why did she do it? Did she torture him? Why didn't she just let him come home?"
Glenn Scrimsher, Jonathan's uncle who had cared for the boy for four years until November 2009 when he went to live with his grandmother, said today that he had always worried about his nephew living with his mother.
"I was worried," said Scrimsher. "Because of my sister's state of mind and her lifestyle was not that of a caring mother who looks after her children."
Scrimsher said he didn't know Jonathan was living with his mother until after the fact. Foster moved back in with Davis just last month.
"The last time I saw him was the day he was leaving for his grandmother's," said Scrimsher. "He was happy to see his grandmother. He called her his granny."
"He loved her very much and he missed her," Scrimsher said.
Gifford, has said that she believed the Houston police waited too long to issue an Amber Alert for the missing boy. The alert was issued on Monday afternoon, nearly three days since he had last been seen.
"Regardless of how this turns out, my goal is to get the Amber Alert law changed," she said. "There should not be criteria for an Amber Alert that depends on whether cops think the kid has run away."
"The cops kept thinking [Jonathan] ran away," she said. "But he had waited too many years to go back with his mama, that's what he wished for on his birthdays, to be back with his mama... That doesn't sound like a kid who wants to run."
Police spokesman Smith defended the timing of the Amber Alert, saying that conflicting accounts of what happened the day Jonathan went missing made the case even harder for investigators.
While he wouldn't specify what the conflicting stories were about in great detail, Smith said that the mother and the boy's stepfather David Davis had originally said that Jonathan was home with a babysitter when he disappeared, but later said he had been at home alone.
ABC Affiliate KTRK contributed to this report.