Council houses should no longer be granted "for life", David Cameron suggested in a public question and answer session in Birmingham.
The Prime Minister said it makes sense for tenants to be given fixed-term deals in future - so they can be moved on if their circumstances change, he told an audience at Austin Court, on Cambridge Street, in the city centre.
He spoke out after being questioned by a mother of two teenagers who said she had slept on a blow-up bed for two years because her local council could not find her a bigger house.
Any move to reform the system would cause "a big argument", he conceded - but said he believes it is right to look at a more flexible system.
The Government is investing more money in social housing, he told the voter.
"But there is a bigger question here, which is: how do we make sure that people are able to move through the housing chain?", he went on.
"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 operate successful "swap" schemes to match tenants, he said.
"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 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.
"Do we want to reform tenure to actually enable people to move through housing rather than seeing it as something that you either get - 'great, I've got my council house' - or you don't get - 'bad, I'm sleeping on a blow-up mattress'.
"So I think a more flexible system - that not everyone will support and will lead to a quite a big argument ... looking at a more flexible system I think makes sense.
"Not talking about existing tenants but, for future tenants, asking: can we relate more the need you have to the housing that you get, making sure we have more social mobility and people can move through social housing, rather than actually see it as something they get for life?"