The UK and the EU will remain the "best of friends" but they will "not be as close as before" after Brexit, the new European Commission president says.
Speaking ahead of talks with the PM, Ursula von der Leyen warned it would be "impossible" to reach a comprehensive trade deal by the end of 2020.
She said if the deadline was not extended it was not a case of "all or nothing", but of priorities.
But Boris Johnson has insisted a deal is possible by December 2020.
The prime minister has also said that the process will not be extended.
After its 31 January exit, the UK will enter into an 11-month transition period in which it will largely follow EU rules but will not have any representation in the bloc's institutions. This period will come to an end on 31 December 2020.
Once the UK leaves the EU on 31 January, the two sides will begin talks on their future economic relationship.
Speaking at London's LSE, Mrs von der Leyen said the EU was "ready to negotiate a truly ambitions partnership with UK" but she warned of "tough" talks ahead.
But she said: "We will go as far as we can, but the truth is that our partnership cannot and will not be the same as before and it cannot and will not be as close as before because with every choice comes a consequences with every decision comes a trade off."
Mrs von der Leyen, a former German defence minister, took over from Jean-Claude Juncker at the start of December. She was a student at LSE in the 1970s.
She added: "There will be tough talks and each side will do what is best for them, but I can assure you the UK will always have a trusted friend and partner in the EU."
She said she hoped the new trading relationship would be based on "zero tariffs, zero quotas, zero dumping".
But she said: "Without the free movement of people you cannot have the free movement of capital and services.
"The more divergence there is the more distant the partnership will be."
Mrs von der Leyen also warned that without an extension of the transition period beyond 2020 "you cannot expect to agree every single aspect of our new partnership".
She called the deadline "very tight".
Opposition MPs have warned that trade deals typically take years to conclude and, with relatively little time available, the UK risks defaulting to World Trade Organisation rules at the start of 2021, potentially leading to damaging tariffs for some industries.
But Brexit Secretary Stephen Barclay told BBC Breakfast that the UK and EU had agreed in the political declaration to do a trade deal by the end of this year and they are "confident" they will do that.
"Of course there will be planning within Whitehall for any eventuality, but we aim to get a trade deal," he said.
"Both sides are clear they want a trade deal, the political declaration says it can be done to that timetable, let's be positive."