Minister Heather Humphreys added: "I was in Northern Ireland yesterday and Arlene Foster did say that she hopes that there will be a softer Brexit".
The date for the new legislative programme to be unveiled came hours before Mrs May is due to host Sinn Fein, the DUP and other parties at No10 in a bid to restore the Stormont assembly after its acrimonious collapse in January.
The party was originally allowed to do so by then Prime Minister Tony Blair to encourage it into the political process but for the decade it has been the joint ruling party in Northern Ireland.
The DUP leader said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".More news: South Korea coach Stielike on the brink after Qatar defeat
Conservative former Prime Minister Sir John, who was crucial in bringing peace to Northern Ireland, raised concerns about the impact of a Tory deal with the DUP.
DUP leader Arlene Foster said there had been "very good discussions" so far and she would travel to London to meet May tomorrow.
Major, who helped lay the foundations of the 1998 agreement that ended two decades of sectarian conflict in Northern Ireland when he was in government, said it would imperil the United Kingdom government's impartial role in the peace process.
Mr Brokenshire said: "It is important to distinguish what happens at Westminster and the votes that take place here, and devolution and the obligations and responsibilities that we hold fast to in relation to Northern Ireland".
"The danger is, however much any government tried, they will not be seen to be impartial if they are locked into a parliamentary deal in Westminster with one of the Northern Ireland parties".More news: Number of Britons granted German citizenship quadruples
The DUP and Conservatives were close to reaching agreement to enable Theresa May to form a minority government and the talks were not in trouble, according to DUP sources.
Some of the other NI parties have said salvaging devolution at Stormont will become more hard if such a deal comes into effect.
'We also made it very clear that we want to make the local institutions work, that we want to deliver an executive that works for all of our citizens, that we would no longer tolerate the denial of rights for our citizens, that we have to make the institutions work on the way in which they are intended'.
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.More news: Manchester bomb investigation team make 18th arrest