The DUP also wants to ensure Sinn Fein can no longer claim salaries, allowances and office expenses while it refuses to take its Westminster seats.
May was meeting the leader of the Democratic Unionist Party, Arlene Foster, on Tuesday to discuss a deal for support in parliament, where May's Conservatives lost their majority in last week's election.
The proposed deal would see the DUP back the Conservatives in votes on the Budget and on any confidence motion while other matters would be negotiated on an issue-by-issue basis.
Different DUP sources say different things about the approach to Brexit.
The DUP is what I would describe as a fairly compassionate party.
Other DUP sources stress a more "practical Brexit" that might permit prolonged membership of the Customs Union.
May's office said Northern Ireland's five main parties would take part, but a spokesman for the DUP did not immediately respond to a request to confirm their participation. "They favour retention of winter fuel payments as a universal benefit".
Sources in the Northern Ireland party indicated today that discussions with the Conservatives are on the verge of being completed - although they have been slowed by the tragic tower block blaze in West London.
Before travelling to the French capital, Mrs May had been leading the talks with the DUP.
As well as its stance on issues such as gay marriage, the DUP is also under scrutiny for a €500,000 donation it received in the run-up to the Brexit referendum past year.
The donation was made by the Constitutional Research Council.
Major's warning comes amid ongoing political turmoil in Northern Ireland.
The DUP have been playing their cards close to their chest, but we know the areas they're talking about because of a DUP plan drawn up in 2015 in anticipation of a hung Parliament.
He stressed he did not share their ultra-conservative views on issues such as abortion and homosexuality, which have caused disquiet among many Conservatives.
Sinn Fein is still committed to powersharing at Stormont as it provides a strategic route to a united Ireland, party president Gerry Adams has said.
Northern Ireland's power-sharing administration, created under a 1998 Good Friday Agreement peace deal, collapsed in January and talks have been going on since a regional election in March to restore it.
Mr Brokenshire insisted the Government would honour its commitments in the Good Friday Agreement and warned that time was running out if power-sharing was to be restored and a return to direct rule from Westminster avoided.