Council houses should be allocated on fixed-term deals rather than being granted automatically "for life", David Cameron has said.
The prime minister added that it was important tenants had the opportunity to move to find work, requiring more flexibility in the system.
Those who succeed in getting better-paid jobs should be encouraged into the private housing sector, he said.
Labour said what was needed was "more secure homes, not less".
Mr Cameron said he expected a "big argument" over the proposals.
The prime minister said fixed-term deals for tenants would allow people to move on if their circumstances changed.
On a visit to the West Midlands, he was questioned by a mother of two teenagers, who said she had slept on a blow-up bed for two years because her council could not find her more space.
Mr Cameron said the government was investing in social housing, but added there was "a bigger question here", which was how to make sure people were able to move through the housing chain.
"At the moment we have a system very much where, if you get a council house or an affordable house, it is yours forever and in some cases people actually hand them down to their children.
"And actually it ought to be about need. Your need has got greater ... and yet there isn't really the opportunity to move."
Many councils ran "swap" schemes to match tenants, he said, adding: "But there is a question mark about whether, in future, should we be asking, actually, when you are given a council home, is it for a fixed period, because maybe in five or 10 years you will be doing a different job and be better paid and you won't need that home, you will be able to go into the private sector....
"So I think a more flexible system - that not everyone will support and will lead to quite a big argument... looking at a more flexible system, I think makes sense."
Any changes would apply to future, rather than current, tenants, Mr Cameron said.
Housing Minister Grant Shapps stressed that the government remained "committed to protecting the security of tenure and rights of those currently in social housing".
But he added: "We should also look at ways of how best to help the most vulnerable in our society, and how to tackle the record 1.8 million households that are now on social housing lists"
Shadow housing minister John Healey said Mr Cameron's words confirmed his party's worst fears about Conservative plans.
"What is needed is more secure homes not less. Before the election Labour warned the Tories had a secret plan to get rid of secure tenancies and they accused us of scaremongering.
"Less than three months later we have the truth.
"This is so important because people highly value the affordable cost and long-term stability of secure tenancy."