The remarks, which were not broadcast but have gained circulation among broadcast journalists, are likely to enrage the right of the Conservative Party when Mr Major had promised a truce with Maastricht rebels.
The incident follows an interview with ITN's political editor, Michael Brunson, last Friday after the Prime Minister had won his confidence vote over handling of the Maastricht Treaty in the Commons. Private discussion seems to have been picked up on a 'live feed' - which made Mr Major's conversation available to the BBC and Sky as well as ITN - and taped by technicians.
According to today's Observer Mr Major told Mr Brunson: 'The real problem is one of a tiny majority. Don't overlook that. I could have all these clever, decisive things which people wanted me to do - but I would have split the Conservative party into smithereens. And you would have said I had acted like a ham-fisted leader.'
Mr Brunson asked the Prime Minister why he did not sack three rebel Cabinet ministers, to which the Mr Major replied: 'Just think it through from my perspective. You are the Prime Minister, with a majority of 18, a party that is still harking back to a golden age that never was (the Thatcher era), and is now invented. You have three right-wing members of the Cabinet who actually resign. What happens in the Parliamentary party?'
When Mr Brunson argued that the Prime Minister had the power to bring in others, Mr Major said: 'I could bring in other people. But where do you think most of this poison is coming from? From the dispossessed and the never-possessed. You can think of ex-ministers who are going around causing all sorts of trouble.
'We don't want another three bastards out there. What's Lyndon Johnson's maxim?' (The maxim is: 'It's probably better to have him inside the tent pissing out, than outside pissing in.')
At no point in the tape did the Prime Minister name the three colleagues singled out for attack. Four Cabinet ministers are regarded as sceptics on Europe: Peter Lilley, Secretary of State for Social Security, Michael Portillo, Chief Secretary to the Treaasury, John Redwood, Secretary of State for Wales, and Michael Howard, the Home Secretary.
But revelations of Mr Major's private opinions, unless proved false, will damage his standing on the right of the party - and undermine his claims to be a sceptic on Europe himself. They also underline the deep divisions which have been created within the Conservatives by the 18-month row over ratification of the Maastricht Treaty.
Downing Street said last night that it 'did not know if this conversation took place and if it did it would have been a private matter'.
Mr Brunson was not available for comment but an ITN spokesperson said: 'Michael Brunson has private conversations with senior politicians all the time and he would never comment on them'.