Mr Ancram said: "We got pretty close to having leader debates in the 1997 election. We are hopeful that this time they will become a reality."
Mr Ancram has written to broadcasting chiefs proposing head-to-head debates between Prime Minister Tony Blair, Tory leader William Hague and the Liberal Democrat leader Charles Kennedy.
Mr Ancram believes that the debates should be shown on the BBC, ITV and Sky television stations, as well as on radio and the internet.
It is not the first time that the Conservatives have called for US-style debates between party leaders.
Strong debater
Mr Hague's strength as a debater and his performance at the dispatch box at prime minister's questions could well show the Tory leader in a good light, Conservative insiders believe.
Mr Ancram said: "We got pretty close to having leader debates in the 1997 election. We are hopeful that this time they will become a reality."
He said that it was right that the public should have the opportunity, during a General Election campaign, to see the three leaders "testing each others' policies and character".
The 1997 campaign nearly saw TV debates, between the then Prime Minister, John Major, former Lib Dem leader Paddy Ashdown and Mr Blair, but in the end no-one could agree on a format.
Downing Street has yet to respond to the latest proposal, but it is unlikely that Mr Kennedy will agree as Mr Ancram's suggestion would bar him from debating simultaneously with the prime minister and the leader of the opposition.
Mr Ancram explained his suggestion by saying that only two party leaders were "in a position to lead the next government".
'Fair' to Lib Dems
He said: "However, we believe the proposal is more than fair in that Charles Kennedy receives equality of time, which the Liberal Democrats would not normally merit."
Responding, Liberal Democrat campaign chairman Lord Razzall renewed his support for leaders' debates during a campaign, but said that three-way debates were preferable to "a series of one-to-one gladiatorial contests on the lines which the Conservatives have proposed".
The Conservatives have also suggested that separate debates should be held in Wales, Scotland and Northern Ireland.
They would involve the Scottish Nationalists, Plaid Cymru and the various Northern Irish parties.