The former owners of The Daily Telegraph have tabled a proposal to restructure its debt to Britain’s biggest high street lender in a last-ditch attempt to regain control of the right-wing newspaper.

Sky News has learnt that the Barclay family submitted an offer to Lloyds Banking Group on Wednesday that would have entailed the bank writing off a portion of the roughly £1bn it is owed.

Further details of the proposal – which followed one last week and was the latest in a series made by the Barclays in recent months – were unclear, although sources said it had been rejected by Bank of Scotland, the Lloyds subsidiary which is owed the money.

Carlyle, the private equity firm which already holds a portion of debt attached to Barclay-backed companies including the online shopping business Very Group, is understood to be involved in the talks with the family.

The Barclay family is being advised by Houlihan Lokey, the investment bank, on the situation.

A family spokesperson said talks with Lloyds “remain ongoing”.

“We hope to come to an agreement that will satisfy all parties,” they added.

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The prospects of a deal being reached by the two sides appear remote, however, given the protracted nature of the talks and the fact that Lloyds had placed the newspapers’ indirect holding company into receivership earlier this week.

Sky News revealed on Tuesday that Lloyds plans to rapidly launch a sale process for the Telegraph newspapers and Spectator magazine, with a bidding frenzy expected to ensue.

Lloyds executives expect the media assets to command a price tag of about £600m, meaning it would still be owed in the region of £400m by the Barclay family even after the proceeds of the Telegraph sale are used to repay part of the loan.

A group of banks including the Wall Street behemoths Goldman Sachs and JP Morgan are vying for the prized mandate to sell the newspapers.

AlixPartners is acting as receiver to B.UK Ltd, a holding company within the Penultimate Investment Holdings Limited (PIHL) Group which indirectly owns the Telegraph Media Group and The Spectator (1828) Limited.

Sky News revealed on Tuesday night that Lloyds is being advised by Lazard on its options for the assets.

The impending sale process would be among the most hotly contested media auctions in Britain for years and is expected to draw interest from billionaires, Tory donors and other media groups.

On Wednesday, Lloyds removed directors appointed by the Barclay family, including Aidan Barclay, the chairman of the newspaper group.

Aidan Barclay is the nephew of Sir Frederick Barclay, the octogenarian who along with late brother Sir David engineered the takeover of the Telegraph in 2004.

Sir Frederick is currently embroiled in a £100m court battle over his divorce settlement.

The Barclays previously owned the Ritz hotel in London, and still own the delivery service Yodel.

Lloyds and Carlyle declined to comment.