The city's medical examiner has yet to determine the cause of death, be it a double homicide or a suicide pact.
The New York Police Department declined to confirm the Times' report.
Detectives tracing their credit card usage discovered that they first went to Washington and then Philadelphia before arriving in NY on September 1, police said.
Chief of detectives Dermot Shea said they were interested in finding out what happened since they were reported missing, and what led them to New York City.
Detectives are now reviewing hotel and restaurant records, video, electronic statements and eyewitness accounts to determine what the sisters were doing between September 1 and October 24, when their bodies were found in the Hudson, a source said.
Police said there were no signs of trauma and it appeared that they were alive when they went into the water.
"Those interviews are really unraveling, in some way, a piece of the puzzle of behind the scenes", Shea added.
On Wednesday, the police department released new passport-style photographs, showing the two young women wearing headscarfs.
On Oct. 31, someone called the NYPD detectives and told them a story "that was haunting him - his words", Shea said: On Oct. 24, the man told the detectives, he was in Riverside Park at about 7 a.m.to exercise, and found the sisters on a playground. Despite the distance, the man believed they were together as their heads were both lowered in their hands as they loudly prayed. She said Tala was visiting Rotana in NY but that she'd lost touch with both about a week before the bodies washed ashore.
It continued that it is not clear how Tala, 16, and Rotana, 22, died, but said there was no information to suggest foul play.
The sisters had recently requested asylum in the United States without giving a reason for the application, the "New York Times" reported, citing police sources.
Now police have discovered that the two sisters who washed ashore were Saudi citizens living in Virginia who may have sought asylum in the US. No one knows where they were staying before their passing.
The case remains steeped in mystery more than a week after the bodies of 22-year-old Rotana Farea and 16-year-old Tala Farea of Fairfax, Virginia, were discovered in upper Manhattan with their feet and waists bound together by duct tape.
In a statement, the consulate said it had appointed a lawyer to follow the case "to avoid inaccurate reporting".
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