The police decision will be sent to prosecutors on Tuesday, who will have 15 days to evaluate the case, a spokeswoman for the attorney general's office told AFP.
A final ruling on the case will be made by a judge.
A spokesman for Neymar said he was not able to comment on the police decision. Sao Paulo police are due to hold a news conference on Tuesday.
Neymar has vehemently denied allegations he raped a Brazilian woman in a Paris hotel in May.
The ugly affair, which has dominated headlines and conversations in the soccer-mad country for weeks, overshadowed Brazil's preparations for the Copa America.
Hosts Brazil went on to win South America's showcase tournament earlier this month without their biggest player, who was injured in a warm-up friendly before the opening match.
The scandal blew up on June 2 when Neymar published a seven-minute video on Instagram, where he had first been in contact with 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 -- without her consent, possibly breaking Brazilian law.
- Police questioning -
The drama quickly snowballed. Extracts of a televised interview with Trindade, in which she accused Neymar of "aggression together with rape," aired just one hour before he was about to enter the pitch for the pre-Copa 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.
As the case dragged on, police filed a defamation suit against Trindade -- who was dropped by multiple lawyers -- after she insinuated the force was corrupt.
"The police are bought, aren't they? Or am I crazy?" she told television channel SBT last month in response to questions over the police investigation of an alleged theft of a tablet device from her home that contained a short video she claims has conclusive evidence she was assaulted.
Despite the seriousness of the allegations, polls have shown that most Brazilians believe Neymar is innocent.
Controversy has followed the Paris Saint-Germain player, who flew back to France earlier this month.
Neymar, who joined PSG in 2017, has made clear he wants to return to Barcelona.
He has yet to feature during PSG's pre-season tour in Asia and French media reported he will miss Tuesday's game against Sydney in China.
