European Commission head Jean-Claude Juncker says whether or not Britain leaves the EU with a deal will come down to a decision by the UK government.
The EU has stressed it is not shutting the door to a Brexit deal and has made itself available for last-minute negotiations but says Britain would need to move considerably to secure an agreement.
With Britain due to leave the bloc on 31 October, the comments by European Commission head Jean-Claude Juncker and Brexit negotiator Michel Barnier were aimed more at sidestepping any blame for the final outcome rather than signalling a deal was in the making.
"I don't accept this blame game that started in London. Personally, I don't exclude a deal," Mr Juncker told the European Parliament's plenary session on Wednesday.
"The risk of a no-deal remains real and basically is going to come down to a decision by the UK government, but will never be the choice - the preferred option - of the European Union.
"That's why I think it is better now to focus on what we can do in terms of concluding that deal, something which is desirable and still, in my view, possible."
Mr Barnier listed three main reasons why the EU could not accept the latest UK proposals on Brexit: customs solutions envisaged for the island of Ireland, the role of Northern Irish authorities, and a lack of legally operable solutions to ensure it all works.
"To put things frankly, we are not really in a position to be able to find agreement with the UK," he said, while adding he would make himself available 24/7 in the coming days to try to seal a deal, which was "still possible" with political will.