The prime minister said such a move could allow more time to sort out Britain’s future relationship with the EU, without needing to activate a controversial contingency plan for the Irish border known as the “backstop”.
While extending the transition was “undesirable”, Mrs May said she was ready to “explore every possible option”.
Mrs May was updating MPs on the state of play in the Brexit negotiations, amid speculation she could be about to face a vote of no confidence amid disquiet over her handling of Britain’s EU exit.
Anonymous MPs were quoted using violent imagery to describe how perilous her position was, comments that have sparked a backlash and calls for the perpetrators to be reprimanded.
In a bid to steady the ship, the PM said a withdrawal agreement was 95% done and called on fellow Tories to “hold our nerve” and get a deal over the line.
Labour leader Jeremy Corbyn said the government was “terminally incompetent”, adding that the prospect of extending the transition showed Mrs May’s administration was an “utter shambles”.
There were difficult questions for the PM, but some indications she may have bought herself some more time.
Steve Baker, a prominent member of the backbench European Research Group of Conservative MPs, said there had been “strong reassurance” from Mrs May on the question of the border “backstop”.
On that question, the PM told the Commons there remained an “impasse” between London and Brussels.
Extending the transition period – which is currently due to run from March 2019 to the end of December 2020 – has been put forward as a potential solution.
Britain and the EU cannot agree on what the backstop – a fallback option designed to avoid the return of a hard border on the island of Ireland – should look like.
Both sides do not want to use it, but it could prove unavoidable if Britain cannot agree a deal on its future relationship by the time the transition period ends.
In essence, the backstop would help bridge any gap.
The EU wants it to apply to just Northern Ireland, while Mrs May wants it to be UK-wide.
So far there has been breaking of this logjam, hence the transition extension emerging as a potential option.
On this prospect, the PM said: “There are some limited circumstances in which it could be argued that an extension to the implementation period might be preferable, if we were certain it was only for a short time.
“For example, a short extension to the implementation period would mean only one set of changes for businesses – at the point we move to the future relationship.”
But she stressed the transition would have to be finished “well before” the end of the current parliament, which is expected in June 2022.
“But in any such scenario we would have to be out of this implementation period well before the end of this parliament.”
The idea is politically perilous for Mrs May, given it would mean sticking with EU rules and regulations for longer and contributing more money to its budget.
So she was at pains to make clear that she would not countenance a scenario in which the UK could remain “indefinitely” in either an extended transition or backstop.
“We would not accept a position in which the UK, having negotiated in good faith an agreement which prevents a hard border in Northern Ireland, nonetheless finds itself locked into an alternative, inferior arrangement against our will,” the PM said.
Responding to Mrs May, Mr Corbyn claimed the government remained riven by infighting.
He told MPs: “The Conservative Party has spent the last two years arguing with itself instead of negotiating a sensible deal in the public interest.
“Their Brexit negotiations have been a litany of missed deadlines, shambolic failure and now they’re begging for extra time.”