In an update to the stock exchange this morning, Media Concierge said it had approached the board with its bid 22 days ago but had received “no substantive engagement”.

It urged National World to consider the 21p per share offer, which represents a 40pc premium to the company’s closing price on Thursday.

Media Concierge said the bid provided a “highly attractive and deliverable opportunity for National World shareholders to realise their investment at a substantial premium in cash”.

Mr Denmark is understood to be frustrated by a lack of direction at National World, as well as its digital strategy. The publisher has said it will produce half of its newspapers using artificial intelligence by the end of the year.

Mr Montgomery, 76, is known for heavy cost cutting at his titles. National World had slashed more than one in four jobs since buying up more than a dozen titles from collapsed publisher JPI Media in 2021.

Mr Denmark started his business in 1985 with the launch of an advertising agency representing media owners. He has since expanded his interests and is the largest regional newspaper publisher in Ireland with 22 titles.

The 69-year-old is also a prominent owner of race horses, racing in both England and Ireland. A non-gambler, he has previously criticised bookmakers’ relationship with the sport.

A spokesman for National World declined to comment.