Foreign Secretary William Hague said there would be a "very, very powerful" case for a referendum if Europe moved towards a more federal system, as expected in response to the eurozone crisis.
But he said the Government wanted to see whether it could negotiate a better relationship between the UK and Brussels, with the return of powers, before putting the matter to the British people.
He told BBC1's Andrew Marr Show:
Asked about the EU's moves towards closer union, Hague said:
Mr Cameron would be setting out his position on a referendum in more detail in the autumn, Mr Hague said.
David Cameron has sought to reassure eurosceptics he is prepared to hold a referendum on Britain's relationship with Brussels - but only when there is a "real choice" for voters.
The Prime Minister insisted that an immediate in/out referendum - which he is under mounting pressure from within his own party to deliver - was not what the vast majority of people wanted.
But, in an article for The Sunday Telegraph, he acknowledged the need to ensure the UK's position within an evolving European Union has "the full-hearted support of the British people".
Our Political Correspondent Lucy Manning reports on David Cameron's attempt to reach out to eurosceptics in his party.
Mr Cameron said he agrees with the "vast majority of the British people" who he said were not happy with the UK's relationship with the EU.
There were large amounts of EU legislation that should be scrapped, he said.
"Put simply, for those of us outside the eurozone, far from being too little Europe, there is too much of it. Too much cost, too much bureaucracy, too much meddling in issues that belong to nation states or civil society or, indeed, individuals," he said.
"Whole swathes of legislation covering social issues, working time and home affairs should, in my view, be scrapped."
Nearly 100 Conservative MPs have written to Mr Cameron urging him to make it a legal commitment to hold a poll on the UK's relationship with the EU during the next parliament.
Influential backbench Tory Mark Pritchard said: "The Tory grassroots and the British people are fed up of 'aluminium guarantees' promising a future referendum on Europe.
"There should be a referendum in this Parliament with events in Europe possibly overtaking all British political leaders."
Mr Cameron's article comes after the latest EU summit to tackle the eurozone crisis ended yesterday with moves towards closer ties in the EU.
At the end of the gathering, he told reporters that he was not in favour of an in/out referendum, leading some observers to think he was ruling out a popular vote altogether.
Former defence secretary Liam Fox will set out his staunchly eurosceptic credentials on Monday when he declares that "life outside the EU holds no terror".
In a speech, the Tory MP will say: "I would like to see Britain negotiate a new relationship on the basis that, if we achieved it and our future relationship was economic rather than political, we would advocate acceptance in a referendum of this new dynamic.
"If, on the other hand, others would not accede to our requests for a rebalancing in the light of the response to the euro crisis, then we would recommend rejection and potential departure from the EU.
"For my own part, life outside the EU holds no terror. I believe globalisation will increasingly force countries to cooperate more closely on the basis of functional commonality rather than geographical proximity. It would, though, given our economic interdependence be to the advantage of all to create a more stable and mutually agreed compromise."