And he insisted the United Kingdom must be able to unilaterally leave any Northern Ireland backstop in the next three years. Foremost was a demand that May seek a "permanent and comprehensive UK-wide customs union".
Housing minister James Brokenshire said on Sunday May would commit to giving parliament another debate on Brexit with the chance to vote on alternative options, if a deal had not yet been agreed and voted upon by then.
She insisted her deal already met numerous conditions he had set.
Brexit is scheduled for March 29 and British Prime Minister Theresa May has not been able to finalise an arrangement with the bloc after her deal was rejected by the British Parliament with overwhelming majority in January.
"This new agreement lays the foundations for the two parties to continue their sound economic and trade relations once the United Kingdom has left the European Union", the Swiss government said in a statement (here in English).
In her letter May argued that her own Brexit plan "explicitly provides for the benefits of a customs union" in terms of avoiding tariffs, while allowing "development of the UK's independent trade policy beyond our economic partnership with the EU".
Mrs Leadsom said: 'I think she's making quite clear that what Corbyn is demanding is actually not as good as what the Prime Minister's deal is offering.
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.
However, BBC political correspondent Iain Watson said it appears there are some potential stumbling blocks to a deal.
Theresa May has rejected Jeremy Corbyn's demand that the rights of British workers will automatically keep pace with those in the European Union after Brexit.
"But, the solution to this has to be to get Jeremy Corbyn, or the Labour Party, or indeed Parliament as a whole, to come behind a deal".
"By getting the changes we need to the backstop; by protecting and enhancing workers" rights and environmental protections; and by enhancing the role of Parliament in the next phase of negotiations I believe we can reach a deal that this House can support'.
She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so.
The Prime Minister's official spokesman said it would give MPs more time to "digest the content" ahead of a series of expected Commons votes on Thursday.
"(It) is to make sure that parliamentarians have had ample opportunity to look at the deal she's putting forward before it comes to that meaningful vote". If not, the vote would be in March, the same month in which the United Kingdom is due to leave the EU.