Sky News has learnt that Daily Mail & General Trust (DMGT) lodged a formal offer last week for the title, which is part of privately owned Dennis Publishing.
DMGT, which is close to landing a £640m windfall from the takeover of Zoopla-owner ZPG, is also understood to be keen to acquire Moneyweek and The Week’s US sister title as part of a deal.
A source close to the auction of Dennis, which was created by the late media tycoon Felix Dennis, said DMGT had not bid for the remainder of the company’s titles, such as Viz and a cluster of computing and automotive magazines.
The listed media company is understood to be keen to promote The Week across its national newspapers and to expand the magazine more aggressively in the US.
Dennis has been put up for sale by the executors of its founder’s estate, with the proceeds expected to be distributed to The Heart of England Forest Charity, which was also set up by tree-loving Mr Dennis.
The charity’s trustees are chaired by Jon Snow, the Channel 4 News presenter.
DMGT is facing competition for Dennis’s assets from a number of private equity firms, including Equistone, HIG and Inflexion.
Some of the bidders have lodged offers for the entire business, while others have identified specific titles that they want to buy.
Epiris, another financial investor which owns the TV Times publisher Time Inc UK, has also been linked to a bid for the Dennis titles.
Both Dennis and Time Inc UK have provided evidence of the toll being exerted on print media groups in recent years amid growing pressure on advertising revenues as readers increasingly shift online.
In 2009, Dennis ceased publication of Maxim UK’s print edition following a catastrophic decline in sales in the lads’ mags? category.
However, The Week, which is likely to be valued at well over £100m, has seen its circulation rise steadily even as the newspaper titles it summarises have seen demand shrink at a rapid rate.
Figures produced by PricewaterhouseCoopers suggest that print advertising revenue for consumer magazines will fall to $6.7bn in the US by 2021, less than half the $13.6bn that magazines took in 2012.
Print circulation sales are projected to drop 23% to $6.1bn over the same period, and industry trends are broadly similar in the UK.
The Dennis auction is being handled by Livingstone Corporate Finance, an advisory firm.