Bratton, who presided over a record drop in crime in the 1990s, said he would be "pleased and honoured" to provide services and counsel in any capacity, adding that he had worked with British police for nearly 20 years.
The Los Angeles Times said Bratton, now overseeing a private security firm, could head London's Metropolitan Police, a job he had long coveted.
The idea of nominating Bratton has met with strong resistance from British police authorities and others who said the head of Scotland Yard should be a Briton.
Cameron, though, told Parliament last month that non-citizens should be considered for the post.
Yesterday he said he wanted to look at cities that had fought gangs "by engaging the police, the voluntary sector and local government".
He said he was "acting decisively to restore order on our streets", as police raided houses to round up suspects from four nights of unrest in London and other English cities.
Steve Kavanagh, the deputy assistant commissioner of London's Metropolitan Police, admitted the force initially did not deploy enough officers to control the outbreak of violence. "It is clear we did not have enough numbers on duty to deal."
Cameron is under pressure from different quarters to ease his austerity plans, toughen policing and do more for inner-city communities.
Labour leader Ed Miliband took care not to blame the Government's planned cuts directly for the violence, but told the BBC: "The cuts that are being made are very bad for our society.
"The events of the last few days have been a stark reminder to us all that police on our streets make our communities safer and make the public feel safer."
Hugh Orde, president of the Association of Chief Police Officers, said "honest conversations" were needed with the Government about its spending plans. "It's the 20 per cent cuts in the present spending period that will lead to less police officers."
Cameron, though, cast rioting and looting as a "deep moral failure", and laid much of the blame at the door of parents whose children took part.
Parents and children alike must be made to take greater responsibility for their actions, he said.
"This is a time for the country to pull together," he said. "We will restore a stronger sense of morality and responsibility - in every town, in every street and in every estate."
Rejecting claims that poverty fuelled the disturbances, Cameron said the root causes of this week's violence were cultural, not economic. "This is not about poverty, this is about culture.
"The young people stealing flat-screen televisions and burning shops, that was not about politics or protest, it was about theft."
Cameron said family breakdown and poor parenting had played a significant role.
"In too many cases, the parents of these children - if they are still around - don't care where their children are or who they are with, let alone what they are doing," he said.
"The potential consequences of neglect and immorality on this scale have been clear for too long, without enough action being taken."
Conservative MPs are demanding tough punishments for offenders, and Cameron insisted that severe penalties would be imposed.
Addressing offenders directly, he said: "We will track you down, we will find you, we will charge you, we will punish you. You will pay for what you have done."
- Agencies
Spreading the word
Word of the riots spread quickly via BlackBerry Messenger, Twitter and Facebook. Among messages sent were:
* Everyone up and roll to Tottenham f*** the 5-0 (police). I hope 1 dead tonight.
* Want to roll Tottenham to loot. I do want a free TV. Who wudn't.
* Jewellry Shop In Green Lanes Getting Robbed Right In Front Of My Eyes
