The EU's chief Brexit negotiator Michel Barnier has warned that a year will not be enough to reach a full deal with the UK.
When Brexit takes place later this month, there will be a 'transition period' to allow full negotiations on the future relationship between EU and UK.
However, British Prime Minister Boris Johnson has ruled out an extension to the transition period beyond the end of 2020.
During a meeting in London yesterday, Mr Johnson is said to have "very clearly" told European Commission President Ursula von der Leyen that he does not want an extension.
With formal trade talks only able to get underway once the UK formally leaves the EU on 31st January, that will leave only 11 months for a deal to be reached.
Michel Barnier said that means the "timeframe is hugely challenging" and that a "new clock is ticking".
Speaking in Sweden, Mr Barnier said: "We will strive for a partnership that goes well beyond trade and is unprecedented in scope: covering everything from services and fisheries, to climate action, energy, transport, space, security and defence.
"But that is a huge agenda. And we simply cannot expect to agree on every single aspect of this new partnership in under a year."
He added: "If we want to agree on each and every point of this Political Declaration - which would lead to an unprecedented relationship - it will take more than 11 months.
"So we are ready to do our best, to do the maximum, in the 11 months, to secure a basic agreement with the UK... but we will need more time to agree on each and every point of this Political Declaration."
He said he believes the negotiations should prioritise a number of aspects - including building a "very close security relationship" and an "economic partnership based on a level playing field".
Mr Barnier added: "I will approach the negotiations of this next phase with the same respect, the same objectivity, the same calm and the same patience.
"Brexit is a school of patience."
Mr Barnier led the EU's negotiations on the withdrawal agreement, and has been appointed as the Head of Task Force for Relations with the United Kingdom in Ms von der Leyen's European Commission.
The Task Force will focus on dealing with "strategic, operational, legal and financial issues" resulting from Brexit.