The proposal was made by EU Brexit chief Michel Barnier as he met member states while thrashing out the final details of the withdrawal deal.
It would give Britain the option of remaining in the single market and customs union until the end of 2022.
This would allow negotiators nearly four years to strike a future trade deal and avoid need for the Irish backstop but would infuriate Brexiteers, as it would mean continued freedom of movement and paying membership fees of up to £10billion a year.
EU Brexit chief Michel Barnier has proposed the UK be given a two-year extension to remaining fully inside the single market in order to ensure a smooth Brexit
Mrs May has said she may ask for an extension to the post-Brexit transition period, which currently ends in December 2020, but only for a ‘few months’.
According to one diplomat at yesterday’s meeting, member states voiced their approval to extend until December 2022 to give ‘people and businesses certainty’.
The diplomat said: ‘You have to provide as much clarity because businesses and people are affected in their everyday lives.’
As it stands, the transition period will begin on March 30 after leaving and last until December 2020.
The UK will be able to extend it in July 2020 if a trade deal is unlikely by the end of that year.
But the length of time has not yet been tied down and is the only piece of the agreed divorce deal left blank.
The withdrawal agreement states the transition period could be extended ‘up to 31 December 20XX’, with a date to be agreed and inserted before Sunday’s summit.
The diplomat added: ‘Michel Barnier proposed December 2022 and the member states were OK with that.
‘The British have not proposed anything as far as we know.’
Mrs May has also said she may ask for an extension to the post-Brexit transition period, which currently ends in December 2020
Britain’s other option in July 2020 would be to switch to the so-called Irish backstop at the end of that year, which would mean leaving the single market but entering into a joint customs union which the UK could not unilaterally pull out of.
This would last until a trade deal is done which prevents a border emerging in Ireland.
Spain is also said to have raised concerns at yesterday’s meeting with Mr Barnier about the scope of the withdrawal agreement in relation to Gibraltar.
It comes ahead of today’s meeting of member states’ foreign ministers in Brussels to sign off on the deal.
Over the weekend negotiators were also thrashing out the final details of the political declaration on the parameters of the future relationship.
That document will now expand to around 20 pages from the original six published last week.
Both sides are expected to publish a final version of the text tomorrow.
The developments came as Brussels’ top eurocrat, Martin Selmayr, hit back at accusations from former Brexit secretary Dominic Raab that he wanted to punish Britain by losing Northern Ireland.
Mr Selmayr, the EU Commission’s secretary-general, said: ‘Mr Raab and I never met. This may explain why he does not say the truth.
The European Commission is working day and night to help ensure an orderly Brexit.’
Meanwhile, a key ally of German Chancellor Angela Merkel repeated warnings that the Brexit deal cannot be renegotiated.
‘We do not see space for further negotiation,’ said Norbert Rottgen, chairman of the German parliament’s foreign affairs committee.