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European Commission President Ursula von der Leyen said no deal was the most probable end to "difficult" talks.
And the UK prime minister argued the EU needed to make a "big change" over the main sticking points on fishing rights and business competition rules.
The Sunday deadline was set by the two leaders after months of talks failed to achieve an agreement.
If a trade deal is not reached and ratified by both sides by 31 December, the UK and EU could impose taxes - tariffs - on each other's goods.
This could lead to higher prices, among other changes