This is despite Mr Corbyn repeatedly saying there should be a general election if Mrs May can not get a deal through Parliament.
The prime minister queried his call for the United Kingdom to stay in a customs union with the EU - but welcomed more talks with Labour on a Brexit agreement.
In response to Mr Corbyn's letter, Mrs May said she looked forward to Conservative and Labour teams meeting soon to consider "alternative arrangements" to the Northern Ireland backstop.
Brexit Secretary Stephen Barclay is meeting European Union chief negotiator Michel Barnier today and Foreign Secretary Jeremy Hunt will visit Paris and Warsaw for talks this week.
Foremost was a demand that May seek a "permanent and comprehensive UK-wide customs union".
She said the existing Political Declaration - the part of the Brexit deal setting out the goals for the future UK-EU relationship - "explicitly provides for the benefits of a customs union - no tariffs, fees, charges or quantitative restrictions across all sectors and no checks on rules of origin".
"I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deal?"
It also recognises the development of the UK's independent trade policy, she added.
She also questioned whether the call for completely "frictionless" trade would mean reneging on Labour's commitment to end free movement by requiring single market membership.
Liz Truss, the chief secretary to the Treasury, refused on Sunday to rule out resigning from the Cabinet if May switches position and backs a customs union. She told Sky's Sophie Ridge on Sunday: "I absolutely do not think that should be our policy".
The government announced on Sunday that parliament might not be given the chance to vote on its Brexit deal until March.
In the interview Sir Keir described Mrs May's approach as "reckless" and "blinkered" and blamed her "tunnel vision" for the devastating defeat suffered last month when MPs threw out her Brexit deal by a record 230 votes.
However, there is no commitment to hold a binding vote on the deal itself by the end of the month.
Pro-EU Tories Heidi Allen and Sarah Wollaston both said ministers should "step up" this week to prevent a no-deal Brexit.
The move is in response to fears that Mrs May is engaged in a "cynical" attempt to run down the clock and leave politicians with a stark choice between her deal of crashing out on March 29. 'There needs to be a day when Parliament says that's it, enough is enough'.
Asked if May thus realised she needed more Labour votes, Stewart said: "Certainly, the maths suggest that to get this through we're going to need support from all around the house".
Liberal Democrat leader Sir Vince Cable said a further delay was "deeply insulting to the country and to Parliament".