PM wants curbs on migrant benefits
Mr Cameron also indicated he would like tighter restrictions on the ability of citizens from new members of the EU to come to the UK looking for work.
In an interview with The Times the Prime Minister also hailed the UK's "good rate of growth" and indicated that his 2015 election pitch to voters will be a promise to complete the work of repairing Britain's battered economy.
The Prime Minister is set to make a referendum on Europe a key pledge in his 2015 manifesto, with the vote due before the end of 2017 after a period of negotiation with Brussels and leaders across the continent about a new settlement for Britain.
Speaking about his efforts to forge a consensus with German chancellor Angela Merkel and other leaders he told The Times: "Could the whole problems of immigration, problems with welfare tourism .... be part of ... making sure that we have a European relationship that works for Britain? Yes of course it can.
"We should consider all of these things. I think we particularly need to look at the rules on benefits. One of the advantages of British membership of the EU is that British people go and live and work in other countries.
"But I think there is a problem with people living (here) and not working."
Mr Cameron said the "transitional controls" which place restrictions on new member states had been "absolutely vital and we need to look at what more we can do on that front".
But he acknowledged that there was nothing that could be done to stop the restrictions on Romanian and Bulgarian migrants from expiring in January.
The Prime Minister gave an upbeat assessment of the economy, claiming that the UK would be held up as an example of success at the G20 summit or world leaders in St Petersburg.
He said: "My first G20 was in Toronto in 2010 and I'm sitting around the table with the largest budget deficit, the biggest crisis in my banking system and the economy most in need of sea change, and I'm going to be able to turn up to this one, three years later, with UK specifically mentioned in the communique, singled out, as showing a good rate of growth this year."
In a foretaste of the next election campaign he added: "I think we'll be able to say in 2015 'of course we haven't finished the job, the deficit is down by a lot - re-elect us and we'll complete the work.
"'Of course we haven't got everyone off welfare and into work but we have massively turned round the welfare system, re-elect us and we'll finish the job'.
"The British public knew this was never going to be easy, We were elected on the premise of saying 'it's going to be tough'."