Adverts for junk foods would not be shown on television before 2100GMT as part of a government plan to tackle obesity.
Most children watch TV until 9pm, Ofcom said
Manufacturers and advertisers will be urged to agree a voluntary code of regulation, according to reports in two Sunday newspapers.
The proposal is contained in the government's Public Health White Paper, to be published this week.
Other measures include a new "traffic light" labelling system identifying unhealthy foods.
This White Paper had been expected to back a ban on advertising junk food during children's TV hours.
'TRAFFIC LIGHT' PROPOSAL
Red light: Fatty, salty or sugary foods, to be eaten sparingly
Amber light: Fatty but nutritious, to be eaten in moderation
Green light: Fruit and vegetables, to be eaten often
But Ofcom figures showing 70% of children's television viewing takes place between 6pm and 9pm prompted a move toward wider restrictions, reports said.
The Independent on Sunday said Health Secretary John Reid believed he would have public support for the move, which would ease concerns over the growing level of childhood obesity in Britain.
Some large food and drink producers have already begun reducing the number of television advertisements shown, it said.
The paper cites research showing there had been almost 10,000 fewer junk food adverts aired in the past year, compared with 2003.
The proposed ban would include products high in fat, salt or sugar.
This would not only take in burgers, crisps and soft drinks, but would also target certain breakfast cereals and even fish fingers.
The White Paper favours a "traffic light" labelling scheme for foods, according to The Observer.
Unhealthy foods would receive a red label, while healthy choices such as fruits and vegetables would attract a green label.
Nutritious but high-fat foods, such as cheese, would be given an amber label, the newspaper said.
The system would be voluntary, however supermarket chain Sainsbury's has announced it will introduce its own coloured logos to signify healthier options from January.
Its system will use red, amber and green symbols to designate high, medium or low levels of salt, fat, saturated fat, added sugar and calories.
Rival chain Tesco is looking into a traffic light system based on dietary targets from the World Health Organisation and the Committee on Medical Aspects of Food and Nutrition Policy.
The Food Standards Agency is due to publish the results of a study into the various "at a glance" nutritional labelling schemes.
Some foods will get a green light, while others will receive red
The White Paper is also expected to recommend the NHS pays for patients to see personal lifestyle gurus to help them give up smoking, lose weight and live more healthy lifestyles.
And more partnership working is set to be encouraged between schools, charities and community groups to encourage children to think about health.
Peter Hollins, of the British Heart Foundation, said he would welcome moves to curb the promotion of junk food and introduce a traffic light system.
"The key thing is not to compel people to do things but encourage them."
And he added: "We would also want to see something done about snack machines at school."
Andrew Lansley, Shadow Health Secretary, said: "The government have been all talk on public health for the last seven years.
"Now they're reaching for a ban on advertising junk food when their own advisers, the Food Standards Agency and Ofcom have said that it is unlikely to be effective."
He also warned the food industry would not find a traffic light labelling system helpful, as it would attack red lights to many staple foods, such as cheese.
"What the industry is working towards is a system of labelling, showing how foods would represent parts of recommended daily amounts of calories, fats, salts and sugar.
"It would be better now for the government to work with industry towards a single solution, implemented by the industry rather than imposed by government."