EU leaders last week signed off on the first stage of Brexit negotiations and talks on a transition period are due to start in January...
"Until the end of 2020 seems indeed like a natural end point for that implementation period or transition," said Stefaan De Rynck, senior adviser to the European Union's chief Brexit negotiator Michel Barnier.
In a speech to the Chatham House think-tank in London, he added: "Our goal is to make sure the future relationship is in place in January 2021."
He also said that during the transition, "new EU rules that come online will need to be applied in the UK. No cherry picking or what one could call a buffet-style transition".
EU leaders last week signed off on the first stage of Brexit negotiations and talks on a transition period are due to start in January, with Britain hoping for an agreement on the main principles by March.
Speaking in the House of Commons on Monday, Prime Minister Theresa May said she hoped discussions on the transition and future relationship would begin "soon".
But she faced opposition from hardline eurosceptics in her Conservative Party over the terms of the transition, with several asking her whether Britain will actually be leaving the EU in March 2019 as planned.
May has accepted the continued jurisdiction of the European Court of Justice in the transition, and also signalled she would agree to the EU's demand that Britain hold off signing trade deals with non-EU countries.
"We will prepare for our future independent trade policy by negotiating -- and where possible signing -- trade deals with third countries, which could come into force after the conclusion of the implementation period," she said.
However, Conservative lawmaker Jacob Rees-Mogg said the EU's "rather hostile" proposals would "make the United Kingdom in the transition phase no more than a vassal state, a colony, a serf of the European Union".
His comments echoed those made at the weekend by Foreign Secretary Boris Johnson, a leading campaigner for Brexit in the June 2016 EU referendum.
May responded that "a negotiation is between two parties", stressing the transition would provide continuity for businesses and individuals until the future relationship could be resolved.
She repeated that Britain would be leaving the EU's single market and customs union, but said the transition arrangements were "a practical matter that most people will understand and appreciate".