A source said the suspect is in his 20s and lives in East New York, and that he has been a person of interest in the case for a few months.
A news conference is expected Sunday at 11:30 a.m.
"We know they have the person of interest in custody. That's all I can confirm right now," said Karina Vetrano's father, Phil Vetrano.
The medical examiner's lab has matched DNA evidence from the crime to the DNA profile of a suspect, a source says.
Vetrano's parents spoke out Thursday, trying to renew momentum in the case on the six-month anniversary of the murder.
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Karina Vetrano left her home for a jog around 5 p.m. on August 2nd, 2016. When she failed to return, family members reported her missing and started searching for her.
Vetrano's body was found around 9 p.m. by her father about 14 blocks from her home, in the marshes of Spring Creek Park, off 161st Avenue and 78th Street. She was about 15 feet off the trail.
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The medical examiner's office performed an autopsy and ruled Vetrano's death a homicide, saying she was strangled.