Newspaper tycoon Richard Desmond has won the financial backing to bid for the Telegraph titles, it is reported.
The Telegraph is the UK's best-selling broadsheet
Mr Desmond, who owns the Express newspapers and a string of top-shelf magazines, has the support of HBOS and HSBC banks, the Sunday Times said.
Telegraph owner Hollinger, hit by revelations of irregular accounting, is considering selling some of its assets.
News of the accounting problems led to the shock resignation of Hollinger chief executive Lord Black last week.
Lord Black quit last week after it emerged that he and other senior bosses had received $32m without the approval of the firm's audit committee.
Four Hollinger directors stepped down on Friday as the crisis deepened.
The firm, which is facing an investigation by US regulators, said on Friday that it had paid too little income tax and overstated its earnings as a result of the unauthorised payments.
The money came from so-called non-compete fees paid by buyers of Hollinger publications in return for an undertaking not to launch new rival titles.
Lord Black resigned as Hollinger chief executive last week
The revelations have angered Hollinger shareholders, who argue that the payments should have been ploughed back into the company.
A number of UK media groups have been named as possible buyers of the Telegraph titles, which include the Daily Telegraph, Britain's best-selling broadsheet newspaper.
But Mr Desmond, who co-owns a printing plant with the Telegraph Group, is seen as the front-runner.
Conservative leader Michael Howard is reported to have sought assurances from Mr Desmond that the Telegraph papers would retain their right-wing editorial line in the event of a successful takeover.
However, a takeover of the Telegraph titles by the owner of the Daily Express and the Daily Star is likely to trigger an inquiry by UK competition watchdogs.
A separate report in the Observer newspaper suggested that Lord Black, who retains the post of non-executive chairman at Hollinger, is not in favour of selling to Mr Desmond.
The Observer quoted Lord Black as saying that Mr Desmond was "not at the front of the queue".
And some analysts believe that a sale is unlikely to go through until Hollinger has clarified its financial position.
"I can't see why potential buyers are going to go forward unless someone can represent to them that these are the right financials," said Morton Pierce, mergers and acquisitions expert at New York based law firm Dewey Ballantine.