The date is in line with European Union chief negotiator Michel Barnier’s timetable and there is rising speculation the Government will accept it.
Theresa May wants the EU to agree an implementation period to phase in changes for “around two years” after the official Brexit date of March 29, 2019.
December 31, 2020 would be three months shy of two years, but sources suggested the Government was ready to sign up to it.
It would coincide with the end of the EU’s current seven-year budget cycle and save wrangles over what Britain should pay if it stayed in for the first three months of 2021.
The UK and the EU aim to agree the broad terms of the transition phase next month.
A Whitehall source said: “The EU timetable is the working assumption and no one seems too upset by that.”
Brexit Secretary David Davis has indicated he would be content with the shorter period provided there was time to get all the necessary work done.
Leading Brexit backer and ex-minister Iain Duncan Smith said: “The sooner we can get this done, the better. What everyone needs is certainty, not a ‘never-end-um’.”
Fellow Tory MP and Brexit campaigner Peter Bone said: “December 2020 seems a perfectly sensible date. I’m not sure why the Government hasn’t just said ‘yes’ already.”