The former cabinet minister, who was brought back as party chairman when William Hague became Tory leader in 1997, predicted Labour would win a second term when he addressed the Cambridge Forum, a debating society at Cambridge University.
His comments will embarrass the Tory leadership but reflect the private views of many senior figures in the party. One insider said last night: "Everyone is talking about whether William will hang on as leader if we lose, and how well he would have to do to keep his job."
Despite public declarations that the Tories can win the next election, some frontbench opposition spokesmen believe the best they can hope for is to cut Tony Blair's 177-strong majority to about 50. Even the most optimistic Tory MPs speak of securing a hung Parliament.
Lord Parkinson, who won a landslide victory as party chairman in the 1983 election, told the Cambridge students he believed that Michael Portillo would be made Tory chairman after returning to the Commons in this month's by-election in Kensington and Chelsea.
Heaping praise on Mr Portillo, Lord Parkinson described him as "very able, very bright, he has a coherent set of beliefs". "He was the best Defence Secretary we've had in many years. He's an outstandingly capable person. An excellent minister and debater, with joined-up politics. Parliament doesn't have too many of them."
He went on: "I think William Hague will make him chairman of the party and they'll make an excellent combination."
His comments are significant because Lord Parkinson remains a leading figure amongst the party's Thatcherites. His praise suggests that he still regards Mr Portillo as a future Tory leader.
Lord Parkinson urged the former deputy prime minister Michael Heseltine to bow to Eurosceptics by standing down at the next election. And he said that the former chancellor Kenneth Clarke had "to acknowledge that he'll never come back as a great political figure".