They are highlighting a USA Today Sports investigation which suggested that Lochte's key claim that he was ordered to hand over money at gunpoint was true - and that the amount of money was out of keeping with the actual damage done by the drunken swimmer.
Friends are also suggesting that there is still security footage missing from the film released by police and say it is likely to show security guards did not act in the way police described.
Lochte is now gearing up to appear in Dancing with the Stars, meaning a return to Brazil would be problematic. He is reported to a be a frontrunner to take part.
It is unclear how or whether the Brazilian judicial authorities could enforce the police demand that he be compelled to return.
A crime with a maximum sentence of six months is not serious enough to be the subject of extradition, with the U.S-Brazilian treaty for extradition covering only serious alleged crimes.
However the Brazilian authorities could make it almost impossible for Lochte to leave the U.S. by placing a red 'wanted' alert on his passport through Interpol, meaning that he would be arrested if he entered a country which has a treaty with Brazil which would allow extradition for false statement allegations.
And he is separately facing a civil action there by the owner of the gas station.
The 12-time medal winner is facing punishment by the US Olympic Committee after it emerged that he had vandalized a gas station following a wild night out with three fellow swimmers and that his account to the public and to police was untrue.
He issued a tearful apology in an interview with Matt Lauer on NBC, saying he 'over-exaggerated' but has not admitted that he was not robbed.
Although his team mates were detained and questioned after damning security footage from the gas station debunked the robbery claims, the 32-year-old had already fled to the US.
Clemente Braune, the police chief behind the report, said: "We will depend on this measure of cooperation, but he has to come to Brazil and give evidence to a court."
The police chief added Lochte could yet be sued by the gas station owner for the damage, both in civil and criminal court.
Police said that the group ripped down a sign and broke items inside a bathroom.
"(The owner) has set up an appointment to come give a statement. If he wants, a new process can be opened in court. He could sue Ryan for criminal damage and could also start a process in the civil courts, asking for compensation," said Braune.
"That means, in the end, he could be facing charges on three fronts."
Jimmy Feigen, the other swimmer who has admitted to lying to police, is free from any further action having paid a fine of $10,000 to settle the charges that allowed him to leave the country.
The other two swimmers who were present that night, Gunnar Bentz and Jack Conger, have been cleared of any wrong doing.
Lochte's camp are likely to offer a much more aggressive defense of his actions in the wake of the police move - which has to be approved by a prosecutor.
They have made clear that he genuinely believed he was being robbed and have suggested that the disparity between the value of the damage and the amount of money he was asked to hand over by at least one armed security guard who had drawn his weapon meets the legal definition of robbery.
Friends also say that police have not been clear on whether the security guards - who were apparently off-duty officers - were authorized to carry and draw firearms; and that police did not release all available CCTV footage from the gas station.
Lochte has been widely ridiculed as Lyin' Ryan in the wake of his dramatic account crumbling.
He initially said the four swimmers' moving can was brought to a halt - and maybe even sideswiped - by a gang of armed robbers who posed as policemen and pressed a cocked gun to his head when he refused to comply.
All those details turned out to be untrue and Lochte and the other swimmers now agree with most of what police revealed: that the four drunken swimmers had urinated behind a gas station, vandalized it, argued with security guards, handed over money to them, and left for the Olympic village.
A court case centering on false statement charges would focus on whether Lochte's key claim about being robbed was close enough to what actually happened as to be truthful, as that would be the only way his defense lawyers could fight off the charges.
