Jonathan Faull, who is leading the Commission's negotiations with the UK, said it wanted a deal in February but it would be up to heads of state.
He said the Commission would not accept anything that threatened the "four freedoms" - including freedom of movement - the EU was founded on.
And negotiations had been "difficult".
But he suggested it may be possible to get a deal on the UK's reform demands without treaty change.
He said "expectations have been raised" that a deal will be sealed next month.
"There is momentum leading to a very good prospect that agreement will be reached rather soon," Mr Faull told members of the European Parliament in Brussels.
"It was quite clear in December the leaders wanted to resolve this issue but would take the time necessary to do it," said the senior EC official.
He told MEPs that the EU referendum campaign in the UK had already begun "in earnest", but would continue on a more formal basis once the renegotiation process had finished.
He added that the final status of the deal will depend on the substance of what is agreed, but that there are a "range of possibilities", from a "simple declarative statement" from EU leaders, to legislative or treaty changes.
He added that there were "many areas," in the Commission's view, that could be settled without treaty change, which would take "a considerable length of time".
UK cabinet minister Chris Grayling has said remaining within the EU under the UK's current membership terms would be "disastrous".
The EU was heading towards closer integration - a path the UK "will not and should not follow", the leader of the Commons wrote in the Telegraph.
It is being seen as the first sign of a minister preparing to campaign to leave the EU in the UK's referendum.
A government source said Downing Street was "very relaxed" about the article.
David Cameron is to allow ministers to campaign for either side of the debate.
Timeline: What will happen when?
Guide: All you need to know the referendum
Explained: What does Britain want from Europe?
Analysis: Cameron tries to avert slanging match
More: BBC News EU referendum special
David Cameron has a "good prospect" of getting a deal with other EU leaders on his reform demands next month, the European Commission has said.