Britain is already set for a 20-month Brexit transition period once it leaves the EU in 2019.
However, government sources have told the Times that they are to seek an additional transition period for customs and regulations that would effectively extend the transition period to 2023, about seven years after the vote for Brexit.
The additional transition period would be designed to give the government time to create and implement new customs arrangements that would avoid a hard border in Northern Ireland, sources told the paper.
May's government has yet to come up with a proposal that will convince both her own party and Brussels. On Wednesday the chief executive of HMRC, Jon Thompson, told Parliament that the current proposals put forward by the government would take up to five years to implement and cost businesses up to £20 billion a year. EU officials have so far rejected both of the proposals put forward by the UK.
The plan for an extended transition comes as May prepares to face down a Commons rebellion on the customs union. Up to 15 Conservative MPs are considering joining with Labour to back an amendment to the Brexit bill that could force Britain to stay in a customs union with the EU after Brexit.
Government whips are preparing to table an early vote for next month in an attempt to force Conservative rebels to stand down and back the government.
Any extension to Brexit transition arrangements would be highly controversial with Conservative MPs.
One leading Conservative Brexiteer told Business Insider that there would be an attempt to overthrow May if there is any further "backsliding" on Brexit.
"If Brexit isn't delivered there will be a lack of confidence in the government, both in parliament and in the country," they said.
"If that's the case then we're heading for a vote of no confidence in the prime minister and a general election. I would support that vote of no confidence."