EU Commission President Jean-Claude Juncker says he wants a "fair deal" for the UK in Europe and does not rule out making minor changes to EU treaties.
He said it was too early to decide what treaty changes might be necessary.
"I do exclude major treaty changes as far as the freedom of movement is concerned - but other points can be mentioned," he told reporters.
Freedom of movement is a core EU value. The UK Conservatives want EU reforms ahead of any referendum on membership.
Many observers believe that Prime Minister David Cameron would need to get changes to the EU treaties before the in/out referendum he would like to hold in 2017, after renegotiating the UK's membership terms.
The referendum depends on whether the Conservatives can win re-election on 7 May.
Mr Juncker said he did not want Britain to leave the EU, but also did not want Britain to "impose a European agenda which would not be shared by others".
"I do think that we need a fair deal with Britain - but it's up to Britain to put forward their proposals, their requests, their ideas.
"It's up to them to take initiatives and then we'll take them under exam in a very polite, friendly, objective way," he told reporters on a flight back from Ukraine.
Travelling with Juncker - by BBC Europe Editor Katya Adler
Treaty change could be possible, the president of the European Commission conceded, though not on major issues such as freedom of movement in the EU.
All in all, he said, he wanted Britain to get a fair deal.
He insisted that had been his opinion all along and expressed frustration that some in Britain gave the impression he had just recently changed his mind.
Criticism of UK
Mr Juncker accused politicians and sections of the UK press of misreporting his position on treaty change.
"I made it perfectly clear during the [European election] campaign that I want a fair deal with Britain.
"Unfortunately the British government and the British press are not listening and are blind when others are speaking so they did ignore that."
He also complained about a British press report last week, which suggested he had said there would be no treaty change from now to 2019. It quoted an unnamed EU official.
"I am the only EU official to be quoted when it comes to Britain," he insisted.
Mr Cameron is especially keen to change the basis of EU migration to the UK, so that there are stricter rules for welfare benefit claimants.
The European Commission, which acts as guardian of the treaties, argues that there can be no discrimination on a nationality basis in the EU.
A major treaty change would risk creating political difficulties for leaders in the 28-nation EU, and the UK's partners have shown little support for such an undertaking.
The Lisbon Treaty, adopted in 2009, resulted from some eight years of tough negotiations and only got through after a second referendum was held in the Republic of Ireland.
To satisfy Irish concerns, a separate protocol was attached to the treaty.
There is speculation that the EU could adopt a separate protocol for the UK, which could become law when another significant change is made to the EU treaties.
Mr Juncker acknowledged that deepening eurozone integration "could easily lead to treaty changes too".
German Chancellor Angela Merkel has said treaty change is probably necessary to give eurozone institutions such as the European Stability Mechanism a firmer legal basis.
But Mr Juncker also stressed that "policy changes are possible under the existing treaties". National governments, he said, acted without having to change their country's constitution.
Mr Cameron has said freedom of movement in the EU should apply to those who want to work in other EU countries, a Downing Street source commented, after Mr Juncker's remarks.
The prime minister has also made it clear he wants a UK opt-out from the EU commitment to ever closer union, the source said.