Such a dramatic move is unlikely, but the rumours underscore how after six weeks of evidence, the closely-guarded members of the jury - who are set to begin deliberating this weekend - are having to come to terms with the knowledge that failing to convict the officers could lead to a repetition of the worst urban riots in the United States this century.
When the policemen walked free from a state court last year, it set off three days of rioting in Los Angeles and outbreaks of unrest in Las Vegas, San Francisco and Atlanta. Afterwards jurors received threatening telephone calls. Devastated by the outcry, several jurors were forced to undergo months of counselling.
The jury deciding the outcome of the second trial, on civil rights charges in a federal court, differs from the first in several crucial respects. The first was drawn largely from the predominantly white and conservative Ventura County, north of Los Angeles, and included no blacks. The second is drawn from a far larger area of southern California and includes two blacks. In addition, the current jurors are identified only by numbers, so they can't be traced.
None the less, the fear of trouble should be strong enough to encourage the current jurors to convict the policemen this time. The white officers were videotaped kicking and beating Mr King, who is black. A conviction, however, is likely to prompt further claims that a fair trial was impossible. Other evidence suggests there is the possibility of a hung jury.
Legal sources have told the Independent on Sunday that soon after the start of the second trial a hearing took place behind closed doors when one juror was suspected of being strongly biased in favour of the police. The judge concluded that there was no justification for stopping proceedings.
The panel must be unanimous to convict the officers. If it is divided, a mistrial could be declared, which technically allows the authorities to try the officers for a third time, although this is thought to be unlikely.
Several miles away from the federal courthouse in Los Angeles, another jury will be watching, ready to pass judgement on the trial's outcome: the residents around the junction of Florence and Normandie streets in south central Los Angeles.
It is the turf of the Eight Tray Crips gang, marked out by lurid flourishes of graffiti and reinforced by threats, fear and automatic weapons.
It is where Reginald Denny, a white lorry driver, was dragged from his truck by black youths hungry to avenge the first jury's decision. The live television footage of Mr Denny's near-fatal attack shocked the nation - images of a long-haired, stupefied, figure groping around the tarmac after a youth threw a brick at his skull as if it were a coconut. A year has passed since this tawdry patch of Los Angeles saw the start of the riots, but memories are fresh and passions still raw.
'After the second trial ends, it is going to be crazy around here,' said Charles Matthews, 39, a petrol pump attendant at the petrol station on the corner, opposite Bob's Liquor Store. A cousin of one of three youths now awaiting trial over the Denny beating, he was gazing thoughtfully across the street at a wall bearing a scribbled recommendation to the world to 'Fucc (sic) the Police'.
'And it is not only going to be concentrated at this corner. It is going to go up all over LA,' he continued, 'It is going to happen in Watts and in the Mexican areas. It's not only a black thing. It's a minority thing. There are not enough police in LA to handle what will happen. There will be an uproar if they let these cops go.
'I know guys in Watts who have been building up a stash of weapons. The only question they are asking is what they should do with them. I tell you, it's going to be chaos. Some people don't even care what the verdict is. They still want trouble.'
Whether Mr Matthews is right or not is not clear. The chances are that he is exaggerating, even though the city has been engaged in an arms-buying spree and is in a highly jittery state about the verdict in the second trial, which is expected sometime next week. The sheer numbers which the police plan to send on to the streets - at least 8,000 - will deter many from a rerun of last year's mayhem. In the meantime, the decision - and history - rests in the hands of the 12 men and women at the city-centre courthouse.