The Sao Paulo attorney general's office said the police decision would be sent to prosecutor who have 15 days to evaluate the case.
A spokeswoman said a final ruling on the case will be made by a judge.
A spokesman for Neymar said he was not able to comment. Sao Paulo police are due to hold a news conference today.
Neymar has vehemently denied allegations he raped a Brazilian woman in a Paris hotel in May.
The scandal blew up on June 2 when Neymar published a seven-minute video on Instagram, where he had first been in contact with alleged victim Najila Trindade, revealing that he had been accused of rape.
In an attempt to defend himself against the allegations, Neymar's video was accompanied by WhatsApp messages and images of his encounter with Trindade, which were published without her consent.
Extracts of a televised interview later aired with Trindade, in which she accused Neymar of "aggression together with rape".
It was broadcast just one hour before he was about to enter the pitch for the pre-Copa America game between Brazil and Qatar.
Neymar tore his right ankle ligament in the 20th minute, ruling him out of the tournament.
In the following weeks, Neymar was questioned by police over the WhatsApp messages.
He also appeared before police in Sao Paulo, where Trindade had filed her complaint at the end of May.
Police later filed a defamation suit against Trindade, who was dropped by multiple lawyers, after she insinuated the force was corrupt.
