They are hoping to ramp up the pressure on the region’s largest political party to change its stance at a time when its policies on social issues are under renewed scrutiny due to the likely parliamentary deal with the minority Tory government.
An agreement between the Tories and DUP is thought to be close, with Mrs May saying the talks had been “productive” and emphasising the need for “stability” in government.
Also on the cabinet’s agenda were the talks to secure an alliance where the DUP backs the Conservatives on a vote-by-vote basis in parliament, rather than a formal coalition government.
“I can’t negotiate with myself”, he added.
Among other ideas, he said the party should change its name to the Conservative Workers Party and develop a campaigning arm along the lines of Momentum or Vote Leave.
Ms Davidson said: “We do have to make sure that we invite other people in now”.
The newspaper also reports that Mrs May has been “aware” of the secret talks for days but has so far done nothing to stop them.
The Brexit negotiator asked London not to “waste time” and explained that it will take “several months to draw out the conditions of an orderly withdrawal, with hard and sensitive points of discussion”.
The Prime Minister apologised as she faced the backbench 1922 Committee for the first time since a disastrous General Election in which the Tories lost their House of Commons majority.
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”.
Speaking at Westminster, the prime minister did not mention the ongoing deliberations as she addressed MPs but called on parliament to “come together in a spirit of national unity” to deal with the challenges facing the country.
The DUP team left by the “Whitehall exit” to the rear of Number 10, avoiding questions from the assembled media.
“We are impatiently waiting for the negotiating position of the United Kingdom gov (ernment)”.
The two sides will continue what sources have described as “positive” talks on Wednesday, with the expectation that an agreement on a so-called “confidence and supply agreement” is imminent.
Asked about whether Britain could remain in the European Union single market, Mr Freeman said: “What we need to do is look at all the options …”
Theresa May has neared a deal with a Northern Irish Protestant party to save her leadership and confirmed Brexit talks would begin next week, amid calls for her to soften her approach to leaving the European Union.
“It’s going to be hard, there’s no doubt about that, but perhaps an opportunity to consult more widely with the other parties on how best we can achieve it”, he said at a conference in Poland, the Financial Times reported.
May apologised to Conservative MPs on Monday, accepting personal responsibility for failing to win an outright victory and sacrificing the parliamentary majority she inherited from her predecessor David Cameron when she came to power past year following the UK’s vote to exit the European Union (EU).
“I will have a problem with it if money which is being given to Northern Ireland for purposes that are devolved to Wales and Scotland”, he told BBC Radio Wales’ Good Evening Wales programme.