Prime Minister-in-waiting Gordon Brown could still hold a referendum on the future of the EU, Europe Minister Geoff Hoon has said.
Chancellor Gordon Brown becomes PM on 27 June
"Clearly a judgement has got to be made in terms of what is in the final package," Mr Hoon told the BBC.
But the revised EU treaty would have to be in Britain's national interests for the government to accept it, Foreign Secretary Margaret Beckett said.
Germany is pushing for a deal at a leaders' summit this week.
Their planned changes would preserve the substance of the original constitution document.
The UK will not accept "cosmetic change" to the treaty, which was rejected in 2005.
Mrs Beckett added that member states still had "strong differences" over the treaty.
She told the BBC's Sunday AM programme: "We do not want to see a constitutional treaty or a treaty that has the characteristics of a constitution.
"We will look at anything that will tidy up the rule book of the EU now that we are 27 and not 12 or 15 [member states].
"But we will look at it on the basis of does this work for Britain, is this in our national interests and will it make the European Union more effective as an operation."
German Chancellor Angela Merkel wants to steer EU leaders towards a new treaty which will give the EU a "single legal personality" and a legally-binding Charter of Fundamental Rights.
This could give British workers new rights to go on strike.
There is also the prospect of more majority voting including in criminal law and foreign policy - both areas where Prime Minister Tony Blair has pledged to preserve British sovereignty.
The constitution was signed by EU member states in 2004, but was rejected by French and Dutch voters in referendums in 2005.
Prime Minister Tony Blair promised a public vote on the EU constitution in 2004 - before it was rejected by France and Holland, but Downing St has indicated that that has now been dropped.
Shadow foreign secretary William Hague welcomed the news that there could now be a referendum.
"If this is a U-turn by ministers it will be a very welcome one. Labour promised a referendum on the EU constitution and it would be utterly unacceptable for them to break their word," he said.