ABC News had previously reported that the pair had been indicted, but it is up to prosecutors to decide whether to act upon the recommendation, and that step has not yet been taken.
The latest twist comes after Brazilian police said four American swimmers were not robbed at gunpoint at a gas station as they claimed.
There is no immediate word on whether Lochte's and Feigen's teammates,Jack Conger and Gunnar Bentz, who were also involved in the incident, have been indicted. They spoke with authorities on Thursday, while Feigen has not been interviewed by police.
Lochte has maintained that he and his teammates were robbed at gunpoint at a gas station in a Rio suburb after returning from a night of partying.
"No robbery was committed against these athletes. They were not victims of the crimes they claimed," Civil Police chief Fernando Veloso said during an afternoon news conference Thursday.
Veloso said the four swimmers vandalized the bathroom on the side of the gas station, damaging mirrors and other property. He said surveillance video shows employees of the gas station tried to control the situation but that the swimmers went to their taxi and tried to get away.
When employees realized what was going on, security guards asked the taxi driver not to leave and to wait for police. Although Brazilian police had said previously that no guns were involved in the incident, Veloso said security officers at the gas station did use guns to control the situation. The surveillance video does show a man approaching the taxi with an object in his hand, but it's not clear whether it is a gun.
Veloso said the gun involved was a legal weapon used by the security guard.
Veloso said the athletes refused to wait for police to arrive. During that time, a third person offered to interpret and explained to the athletes that they had to pay for what they had done to the bathroom. According to Veloso, they offered to pay in the form of a $20 bill and 100 reals (about $51).
Veloso said in the news conference that one of the athletes had confirmed this version, saying there was no robbery. He added that the video confirms the swimmers were not victims of physical or verbal abuse.
Lochte first recounted a robbery to his mother, Ileana Lochte, who spoke with reporters, a police official told the Associated Press. That led to news coverage of the incident and prompted police attention.
Conger, Bentz and Feigen remain in Brazil, as authorities have ordered the seizure of their passports. A Brazilian judge also ordered Lochte's passport be seized, but he said he has already returned to the U.S.
Brazilian authorities said in a statement Thursday that Conger and Bentz were taken off their airplane. A police source told ESPN Brasil that the swimmers were interviewed for just more than three hours at the airport, with a Brazilian lawyer and representatives from the USOC and the U.S. consulate present.
Stephen Conger, the father of Jack Conger, told ESPN on Thursday that his son slept in a hotel Wednesday night and was guarded by U.S. government personnel. Jack was never under arrest, according to his father. "It's more a political ordeal than a criminal one," he said.
Stephen Conger said the plan is for Jack to be on a plane home Thursday night. He said he's shared text messages with his son but said: "We're as in the dark as anyone about what happened. I don't know if there was a robbery or not."
NBC spoke with Lochte on Wednesday night and reported that he said he had left Rio and already returned home, as originally scheduled.
Lochte backtracked on his initial comments to the network made Sunday, saying the barrel of the gun he had said was placed to his forehead was instead pointed in his direction. He also said the taxi wasn't pulled over but that the swimmers were robbed after making a stop at a gas station.
He said when he was interviewed by police about the incident that no one had suggested he needed to stay in Brazil, nor had any officials expressed doubts over his account of the robbery, NBC reported.
International Olympic Committee spokesman Mario Andrada said during a news conference Thursday that neither Lochte nor his teammates need to apologize for the incident.
"We have to understand that these kids came here to have fun. Let's give these kids a break," Andrada said. "Sometimes you make decisions you later regret. They had fun. They made a mistake. Life goes on."
Andrada's comments were made before the reports that a robbery did not happen.
Information from ESPN's Shaun Assael and ESPN Brasil's Gabriela Moreira was used in this report.
Lochte and Feigen indicted, Conger and Bentz booed
Mark Schwarz reports from Rio on Ryan Lochte and James Feigen being indicted by Rio de Janeiro authorities for falsely reporting a crime. After speaking with police, fellow simmers Jack Conger and Gunnar Bentz are booed on the street.