The new political group would contest Westminster, Holyrood and local elections. It leaves Prime Minister David Cameron with the prospect of having no MPs in Scotland.
At present the Conservative Party has only one MP north of the border. Labour’s landslide victory in the 1997 general election saw the Tories in Scotland wiped from the political map.
In the Scottish parliament the Scottish Conservative and Unionist Party has 15 seats out of a total of 129.
Murdo Fraser is likely to unveil his plan at the formal launch of his leadership bid on Monday. He is seen as the front-runner in the contest to replace Annabel Goldie, the present Conservative leader in Scotland.
Mr Fraser told BBC Radio 4: “I think it’s time we launched a new, progressive centre-right party with a distinct Scottish identity – one that would have a partnership with the UK Conservative Party and in other respects be operationally independent.
“I think that would be much more attractive to many people in Scotland who share our values.”
In an extract from his speech for the formal launch of his leadership campaign, Mr Fraser stresses the importance of the union between Scotland and the other parts of the United Kingdom. He is expected to call for “A new party. A new unionism. A new dawn”.
But Scotland’s sole Conservative MP, David Mundell, the Scotland Office minister, said Mr Fraser’s approach was “simplistic”.
He told Radio 4: “I welcome Murdo Fraser opening up the debate. It helps to have a debate and discussion. But I think that, fundamentally, changing the party’s name is a rather simplistic approach to the issues that we face.”
Labour Ann McKechin, the shadow Scottish Secretary, said it was the policies of Mr Fraser’s party that needed to change: “Murdo Fraser’s scheme is doomed to fail because it is his hard-line and right-wing politics that alienate people, not his party’s internal workings.”
In May 2011 Scottish National Party took control of the Scottish parliament, winning 69 seats at Holyrood. It raised the prospect of the SNP introducing a referendum on Scottish independence within the next five years.