The Delaware Department of Services for Children, Youth and Their Families said Thursday that the state filed a motion in state Family Court in the past week to terminate the parental rights of Giordano, who used to live in Hightstown.
Spokeswoman Kelly Bachman said Giordano has until March 27 to turn up, or her rights will be terminated.
Bachman also confirmed that a separate filing to the same effect was made by a person who wants to adopt Michael DiGirolamo.
Bachman declined to disclose further details about the prospective parent, including whether the person is related to the boy. The Trentonian of Trenton reported the person's name was Annalisa Guidice.
The child has been in foster care since last June, when he was abandoned in the parking lot of Christiana Hospital in Newark, Del., by his father, Rosario DiGirolamo.
The father, according to Bachman, gave up his parental rights when he pleaded guilty in November to misdemeanor charges of reckless endangerment and child abandonment.
In New Jersey, Mercer County authorities still consider DiGirolamo a person of interest in the disappearance of Giordano, who was last seen two days before the boy was discovered.
DiGirolamo had been having an affair with the 27-year-old Giordano at the time of her disappearance, and is now in the process of getting divorced.
Jerome Ballarotto, a Trenton lawyer representing DiGirolamo, declined to comment whether a relative of his client's is trying to adopt the boy. But he did say that DiGirolamo wants to be part of his son's life.
"He is prepared to remain in the child's life. We aren't sure how that's going to happen," Ballarotto said.
There was no answer to a call placed to the Brooklyn home of Rosario DiGirolamo's parents, where he's been staying. Associated Press attempts to reach Guidice were also unsuccessful Thursday.
Stephen Fishbaum, a cousin of Giordano's, was concerned over who might adopt the child, but thought it was the best thing to do. Fishbaum, of Marlboro, said Giordano has been estranged from the rest of her relatives for years.
"I'd like there to be closure. In my heart, she's not here, because she would have definitely, definitely contacted me. She would have contacted me in the last eight months," Fishbaum said.
