Sources told the NYC TV station that the boy made statements linking himself to the killing of 18-year-old Barnard College freshman Tessa Majors.
Police recommend charges of second-degree murder, first-degree robbery and criminal possession of a weapon against the 13-year-old suspect, the source said.
Flowers and candles were left at a makeshift campus memorial and her family said in a statement Friday that they "are devastated by the senseless loss of our lovely and talented Tess".
Majors, 18, walked into Morningside Park Wednesday evening when she encountered the suspect or suspects and was stabbed multiple times at the bottom of the staircase at the 116th Street entrance to the park, police said.
The president of the school, which is part of the Ivy League's Columbia University, called Majors' death "an unthinkable tragedy that has shaken us to our core".
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Bleeding and severely wounded, Majors "staggered" back up the stairs to the security guard booth on Morningside Drive, he said.
Majors died at a hospital.
The NYPD is still searching for two others who may be connected with Majors' death.
A 13-year-old boy has been arrested for the murder of a NY college student, WABC reports.
Juveniles convicted in NY state's family courts can be sent to detention facilities until they are 21 in many cases, and are often released after that.
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Majors graduated high school in May from the private St Anne's-Belfield School in Charlottesville, where head of school David Lourie said she was "a shining light in our community, a good friend, respected classmate, trusted teammate, and creative and passionate musician".
Majors was killed just as the semester at all-women's Barnard College was winding down, with final exams set to begin Friday followed by a month break. One of them slashed her on the chin was a knife. She spent her weekends singing and playing punk rock.
Majors was also interested in journalism and had worked as a reporter for a local paper in Virginia.
"We lost a very special, very talented, and very well-loved young woman", her family said in a statement Thursday.
Lexi Phelan, who met Majors this year at Barnard, shared two classes with her.
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