“Good progress” has been made on a post-Brexit trade deal, but the “last stumbling blocks remain”, says EU chief negotiator Michel Barnier.
Talks in Brussels are continuing, with two weeks to go before the UK leaves EU trading rules.
Earlier, Michael Gove said the UK government would do “everything to secure a deal” with the EU.
He also told MPs they could be called back from their Christmas break to approve a deal if one was agreed.
But leaders from the European Parliament said they would “not be rushed” into approving the deal their end, and would have to see the text of any agreement by Sunday if they were to sign it off by the end of the year.
The European Commission President, Ursula von der Leyen, said on Wednesday a “narrow path” has opened up for the two sides to conclude a deal.
But Prime Minister Boris Johnson’s spokesman said he still viewed no deal as “the most likely outcome”.
The UK left the EU on 31 January, but has remained under many of its rules while the two sides negotiate a trade deal.
If an agreement is not reached by 31 December, the UK will have to trade with the EU on World Trade Organization rules – meaning taxes on goods being bought and sold between the two may be introduced, and could lead to higher prices.
Tweeting after updating European Parliament leaders on the negotiations, Michel Barnier said: “In this final stretch of talks, transparency and unity are important as ever.
“Good progress, but last stumbling blocks remain. We will only sign a deal protecting EU interests and principles.”
Mr Gove told the Commons “intensive talks” were continuing, with “both teams working day and night” to “go the extra mile” in seeking agreement.
Pushed by his Conservative colleague Dehenna Davison on whether the UK would walk away if a trade deal was not “in the best interests of our country”, Mr Gove replied: “My honourable friend is absolutely right.”
He added: “Even if sometimes results are coming later than we might have wanted, I know we will be doing everything in order to secure a good free trade agreement in the interest of the whole United Kingdom.”
“The electors… were clear when they voted to leave the European Union, that we need to do so by 31 December 31, and we will.”
What happens next with Brexit?
MPs are due to break up for Christmas later on Thursday, but Mr Gove confirmed they could be called back to the Commons if a deal is agreed between negotiators.
He said the government would “request that the House returns in order to make sure that we can legislate effectively”.
Although there is only 14 days until the deadline, Mr Gove also said he believed there was enough time for the necessary legislation to pass before 31 December “to give businesses legal certainty”.
But a number of opposition MPs raised issues already facing businesses waiting to discover the outcome of talks.
One Welsh MP, Jonathan Edwards, said: “I was contacted late last night by a businessman in my constituency who is reliant on imports from the continent and he can’t find a haulage firm willing to carriage on his behalf due to the current delays at the ports.
“He’s very concerned unless this issue was resolved his business would not survive into the new year.”
Mr Gove said he would get in touch with the business concerned.