The two sides have been in talks on updating the trade deal since May 2016 and had set the end of this year as deadline to seal the accord.
Hopes were raised after rapid progress on issues including market access and intellectual property during talks in Mexico earlier this month, but high-level negotiators could not close the deal.
"We are very close to a deal but we are not really there yet," said EU Trade Commissioner Cecilia Malmstroem at a news conference with Mexican Economy Minister Ildefonso Guajardo.
Both sides are eager to come to terms and mark a contrast with the bumpy negotiations between the United States, Mexico and Canada on updating the North American Free Trade Agreement (NAFTA).
Uncertainty over the future of that 1994 deal -- which US President Donald Trump has made a ritual of attacking -- is weighing on the Mexican economy, which depends heavily on trade with the United States.
"A strong objective (of a deal this year) has put us where we are, which is close to a deal," said Guajardo, who headed a team of about 50 negotiators from Mexico.
Mexico, which sends some 80 per cent of its exports to the US, is looking to diversify its trading partners to cope with the new political reality across the border.
EU-Mexico trade has nearly tripled to USD 61.7 billion under the deal.
But that is still dwarfed by US-Mexico trade, which came in at USD 523.8 billion last year.
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