In an interview in the Mail on Sunday, David Cameron said he wanted to stop workers resenting people on benefits.
In the article, which comes ahead of an expected speech on the subject tomorrow, Mr Cameron said the existing system was sending out 'strange signals' on working, housing and families.
The Mail quoted Mr Cameron contrasting a couple living with their parents and saving before getting married and having children, with a couple who have a child and get a council home.
"One is trapped in a welfare system that discourages them from working, the other is doing the right thing and getting no help," he said.
Mr Cameron said the welfare system sent out the signal that people were "better off not working, or working less".
"It encourages people not to work and have children, but we should help people to work and have children," he said.
He said that he also favoured new curbs on the Jobseeker's Allowance.
Number 10 admits that David Cameron's proposal to remove housing benefit from young people will not become policy immediately.
A Downing Street source said that Mr Cameron was "starting a debate and setting out some ideas. We are realistic that some of them might not be achievable politically because they're not palatable to our coalition partners.
"We would like to get moving on these as soon as possible but we might not be able to get it done until after 2015."
In recent weeks the numbers of people claiming housing benefit reached five million for the first time.
Labour's shadow work and pensions secretary, Liam Byrne, called it a "very hazy and half-baked plan from the Prime Minister, when what we really need is a serious back-to-work programme.
"You have to remember that housing benefit is available to a lot of people who are in work and perhaps on low incomes, so for a lot of young families with their first feet on the career ladder this plan could actually knock them off the career ladder," he told the BBC.
Shelter pointed out that many young people are estranged from their families and do not have the safety net of family homes.
What do you think of David Cameron's proposals?