The president of the EU commission has suggested there may be scope for Britain to adjust its relationship with the union.
But Jose Manuel Barroso flatly rejected the prospect of a cap on migration from member states.
David Cameron has pledged to renegotiate EU rules and hold an in-out referendum on membership by 2017 if he is still Prime Minister.
He has signalled that one of his aims will be restricting access to UK jobs and welfare when less wealthy countries join the union.
The Tory leader has previously highlighted high levels of immigration after Poland and other A8 states acceded.
In an interview with the BBC's Andrew Marr Show, Mr Barroso - who is due to step down from his post in October - said freedom of movement for labour was a "fundamental principle" of the EU single market.
A cap on immigration to a member state would be a "complete contradiction" of that principle, he insisted.
However, he stopped short of ruling out any changes in the area, saying action was already being taken to curb "abuses" of the system.
Mr Barroso said reforms of EU treaties were "extremely difficult" because they required unanimity, but "sooner or later" the euro area would need change to deepen its fiscal integration.
"I don't see a fundamental contradiction between deepening the euro area... and having some flexibility for the EU, providing the general framework is kept as it is," he said.
"It is possible if there is wisdom on both sides, and if it is a constructive discussion, to come to some agreement."
He added: "I think if there is goodwill, if there is intelligence on all sides, it is possible provided that there is not an attempt to put into question the basic princilpes of our union, the integrity of our union."
Ukip leader Nigel Farage said the remarks showed Mr Cameron was merely "spinning a line" about a renegotiation.
"Here is a man who is trying to convince the general public that he can somehow reform the EU and yet the Commission President has said absolutely no proposals have been put forward and any renegotiation of significance would be virtually impossible as it would require all member states agreeing," he said.
"He also repeated that the free movement of people was not up for grabs. All Cameron is doing is spinning a line back home to try to stay in power."
"What was also startling was Barroso revealing that the EU were waiting to see if Britain's position will change in the next Government. He clearly thinks Cameron is out the back door along with his sham referendum pledge and sham renegotiation promise after the next general election.