In her response in the letter, the Prime Minister said she wanted the Tory and Labour teams to consider "alternative arrangements" to the Irish backstop.
In a letter to the Labour leader released on Sunday evening, the prime minister also dismissed Corbyn's call for the United Kingdom to remain in a customs union with Brussels.
"So he wants a customs union and he is unclear as to whether that means he also wants an independent trade policy".
Britain is due to leave the European Union on March 29, but lawmakers in Parliament have emphatically rejected Mrs May's divorce deal, raising the prospect of a no-deal exit from the bloc unless more parliamentary support is found.
Downing Street said Mrs May's statement, which comes a day earlier than expected, will give MPs more time to "digest the content" ahead of a series of expected Commons votes on Thursday.
"I think it must be pretty obvious that if you are going to have a time limit to the backstop, and I think that would be a very good thing, it's got to fall before the next election".
But May's office published her reply to Corbyn late on Sunday (10 February), showing little appetite for a U-turn which would risk splitting her fractious party by ruling out the scope for Britain to strike its own trade deals around the world.
"That gives that sense of timetable, clarity, and objective on what we're doing with the European Union - taking that work forward and our determination to get a deal - but equally knowing that role that parliament very firmly has", Brokenshire told the BBC.
"It is very clear from the European Union that non-EU members do not have a say in EU trade policy so to pretend that you could do so is a risky delusion".
The Leave campaign figurehead was speaking as Brexit Secretary Stephen Barclay prepared for talks with European Union chief negotiator Michel Barnier as the Government stepped up efforts to secure changes to the backstop, which is created to keep the Irish border open after the UK's withdrawal.
She added: "The fundamental negotiating challenge here is the EU's position that completely frictionless trade is only possible if the United Kingdom stays in the single market".
His intervention came after Treasury Chief Secretary Liz Truss refused to rule out resigning if Mrs May backed a customs union.
He has also faced pressure from some of his MPs to push for another public vote on Brexit.
There appears little prospect of an imminent breakthrough with Brussels, and Mrs May might not bring her deal back for a decisive vote this month.
When asked his view on Labour Party colleagues calling for a second referendum, Sir Keir said: "I say we have got a conference motion on this, we agreed in advance what we would do and we tried to foreshadow the decisions we would have to make and we thought we would have to vote on a deal first, if the deal goes down there would be a general election".