Work and Pensions Secretary Iain Duncan Smith has insisted that the door remains open for Britain to secure its key demand for reform to the welfare system for EU migrants.
In a letter on Monday, European Council president Donald Tusk said there was "no consensus" among the EU's 28 member states over the UK's demand to be able to deny migrants in-work benefits for four years.
Mr Tusk said the other 27 national leaders would need to "hear more" from David Cameron before coming to a conclusion on the issue, which he described as the "most delicate" element of the renegotiation of Britain's membership ahead of the in/out referendum promised by 2017.
The comment was widely interpreted as an indication that concessions may be needed from the Prime Minister, who has himself said that he is "open to different ways of dealing with this issue".
But Mr Duncan Smith said that Mr Tusk's letter was "carefully drafted to say that the door is still open" to discussions on Britain's proposal and he was "upbeat" that Mr Cameron will be successful.
Asked what alternatives to the four-year ban he would personally be ready to accept, the Work and Pensions Secretary replied: "That they agree with us. That's an alternative to the way the EU sometimes goes about its business."
Several European leaders have cautioned that the UK scheme would breach the principle that benefit rules should not discriminate against non-native workers from other EU states.
But Mr Duncan Smith insisted that in private, ministers from countries such as Germany and France had agreed that there was "something fundamentally wrong" about a system which makes migrants eligible to claim benefits immediately on arrival in a country where they have made no contribution to the welfare system.
"As usual, it is the British who have to make the case, but behind closed doors they all agree it is an issue," he said.
Asked whether he expected Mr Cameron to make concessions to reach agreement on a reform package at a Brussels summit in February, Mr Duncan Smith said: "My general sense is that the case is still there and the Prime Minister is still going to make it. I remain upbeat."