"The danger is that however much any government tries they will not be seen to be impartial if they are locked into a parliamentary deal at Westminster with one of the Northern Ireland parties, and you never know in what unpredictable way events will turn out, and we can not know if that impartiality is going to be crucial at some stage in the future".
"I am dubious about it", Major told BBC radio.
He thinks it risks violence returning to Northern Ireland.
The late Martin McGuinness resigned from the Sinn Féin-DUP coalition, triggering the collapse of the regional government under the rules of power-sharing.
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
A potential agreement for the Northern Irish unionist DUP to prop up a minority Conservative government led by Theresa May in Britain is causing anxiety and fear in the province, Irish nationalist party Sinn Fein said on Tuesday.
The Secretary of State said the Government remained "four square" behind the Good Friday deal.
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With her tally of Conservative MPs slashed to 317 in last week's poll, Mrs May needs the backing of the DUP's 10 members to reach the 320 required for a working majority in the Commons.
An Irish government spokesperson said: "They discussed the outcome of the United Kingdom general election and the Prime Minister outlined the proposed supply and confidence arrangement between her party and the DUP". Journalist Owen Jones, who is leading a demonstration in London against the prospect of the DUP in Government, has called it "a menace to LGBT rights and women's rights".
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.
The prime minister, he said, has also "just totally ignored the will of the people of Northern Ireland in terms of Brexit", he added.
Alliance Party leader Naomi Long said: "We have to be practical about these things".
"If that's not possible, the Labour Party stands ready to offer strong and stable leadership in the national interest".
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.
Some of the other NI parties have said salvaging devolution at Stormont will become more hard if such a deal comes into effect. "I think most of the Scottish Conservatives will want to see perhaps some changes with the policy going forward".