The so-called "confidence and supply" government being discussed by the Conservatives and the DUP has sparked widespread criticism due to several controversial views held by the latter on homosexuality and climate change.
He said the Government could not act as a "neutral facilitator" in Northern Ireland, as the Good Friday Agreement envisages, if it was dependent on one of the local parties for its majority in the House of Commons.
The finance ministry declined to comment.
In an extraordinary intervention, Major warned that the deal could cause the peace process, which he played a large part in securing as prime minister, to "unwind" and urged May to avoid risking this at all costs.
Mrs Foster arrived with colleague Nigel Dodds and waved to reporters in Downing Street but refused to be drawn on whether she would agree to a deal on Tuesday.
May is expected to have to agreed concessions in exchange for the DUP's support in no-confidence and government-financing votes, which are essential to keeping a minority government in power.
But then May called a needless election to get a bigger majority in parliament-to "strengthen her hand" in the negotiations with the European Union that are scheduled to begin next Monday, or so she said.
The Conservatives, who have 317 MPs, are looking to strike a deal with the DUP, who have 10.
Play ball! GOP, Dems to battle as 1 _ Team Scalise
Before James Hodgkinson left his home in Belleville, Ill., in March, he sold almost everything he owned from his businesses. Bailey was spotted Friday in the Capitol, on crutches and out of uniform, accepting congratulations from fellow officers.
Gerry Adams of Sinn Fein told May specifically of his opposition to the coalition during a meeting with her at Downing Street: "We have just finished a meeting with the British prime minister and her secretary of state".
'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, ' Cameron was reported by the FT as saying at a conference in Poland on Tuesday.
The DUP is believed to be more favourable to a "soft Brexit" that would keep Northern Ireland's border with the Republic of Ireland free-flowing.
But Stormont parties have a June 29 deadline to end the impasse and reach consensus on re-establishing a devolved administration in the region.
"I confirmed to President Macron that the timetable for the Brexit negotiation remains on course and will begin next week", May said after her meeting with the new French leader, who will be a key player in the Brexit talks.
"I think there will be pressure for a softer Brexit", Mr Cameron added, saying that Parliament "deserves a say" on the issue.
"But we do want to do so in the national interest to give stability to the government and that's why we will be entering these negotiations", she said.