Brussels officials said the talks had not reached a political agreement this week, stalling plans for a deal on high-priority areas this year.
Officials including European Commissioner for Trade, Cecilia Malmström, and Mexican Economy Minister, Ildefonso Guajardo, had met late into the night on Wednesday
But, despite apparent progress, they were unable to seal a deal.
The sides announced today they still had to thrash out solutions to issues like agricultural access.
Both are aiming to update their 2000 trade accord, which covers industrial products, by adding farm produce, government procurement and investment.
They also want to embrace open markets as the US turns inwards under President Donald Trump.
Ms Malmstrom said the two sides were edging towards a deal, with more work needed at the start of 2018.
She said: ”We are very close to a deal, but not really there yet. We can see the skeleton of this agreement.
“We know how to get there, we know what to do.”
Mexico and the EU still have to sort out how much to open up their markets to products that include Mexican beef, sugar, poultry and fruit and EU pork and dairy produce.
They also have to bridge differences over a system to settle disputes between companies and the EU system of protecting region-specific products (GIs), such as tequila.
Ms Malmstrom said: “We started talking about almost 400 (GIs) and there are a couple remaining where we need to find solutions.”
Mr Guajardo also said the two parties were “very close, very near” to revamping their 17-year-old accord and said his country saw some merit in a system that would protect tequila as a Mexican product.
For Mexico, a deal with the EU would be part of a strategy to reduce its reliance on the US, the destination of nearly 80 per cent of its exports.
This has become even more urgent given Mr Trump’s threat to scrap the NAFTA trade deal.
Mr Guajardo said his country was working on six fronts in Latin America, Asia and Europe alongside NAFTA partners Canada and the US.
He said that the two parties should at least reach an outline agreement before Mexican President Enrique Pena Nieto’s term expires towards the end of 2018.
The EU has concluded negotiations with Japan earlier this month to create the world’s largest open economic area.
It could also clinch a deal with the Mercosur bloc of Argentina, Brazil, Paraguay and Uruguay early next year.