Topless models have featured in the Sun for 40 years but the media mogul tweeted that they may belong in the past

For more than 40 years, campaigners have tried to kill off the Sun's practice of printing photographs of topless women on Page 3 – but to no avail.

Yet in a single, apparently off-the-cuff remark on the internet, Rupert Murdoch hinted that he may at last be ready to grant the wishes of generations of opponents whose ranks have included, most famously, the veteran Labour MP Clare Short.

Responding to a fellow user of Twitter who described Page 3 as "so last century", News Corp's chairman and chief executive said that he was "considering" whether he was of the same view.

Murdoch, whose tweets are closely scrutinised for clues to the future direction of his global media empire, commented: "page three so last century! You maybe right, don't know but considering. Perhaps halfway house with glamorous fashionistas."

A News International spokesperson said the company was making no comment in relation to whether the Sun's topless Page 3 could be for the axe.

Suspicion that the upper echelons of News International could have reached a tipping point was fuelled by another tweet from a lifelong Murdoch confidant who was asked what he made of Murdoch's comment.

Les Hinton, a former chairman of News International who resigned from his job running Dow Jones and the Wall Street Journal at the height of the phone-hacking scandal on the News of the World, replied: "@TheSunNewspaper great but Page 3 has jarred for ages."

In the most recent campaign against Page 3, supermarkets across Britain have been targeted by activists as they stepped up their campaign for an advertising boycott of the tabloid.

Members of the campaign group No More Page 3 said it was a sexist relic of an unhealthy 1970s culture that was at odds with the family values promoted by supermarkets.

The campaign, which has attracted more than 64,310 signatures of support on a change.org petition, posted a video on YouTube of interviews about Page 3 with male Sun readers, many of whom said it was degrading and sexist. The group has also held weekly protests outside News International.

Beyond activist circles, the view that Page 3 has had its day has been gaining ground for some time. Ross Brown, a former editor of FHM magazine, said last year : "One of my best friends is the editor of Nuts and we spend much of our time arguing. I think it's just reached a point where it's readily accessible porn, from Page 3 to Nuts. And we're past that."

According to Fleet Street lore, Murdoch is said to have been unhappy when topless Page 3s were introduced by the then Sun editor Larry Lamb in November 1970. However, any latent opposition the proprietor harboured at the time appears to have vanished as the newspaper's circulation rose and the topless Page 3s become closely associated with the brand.

In 1986, Clare Short raised the issue in the House of Commons, leading to supportive letters from women and attacks by the paper.

At the Leveson Inquiry, Sun editor Dominic Mohan said a particularly nasty piece headlined "Fat, jealous Clare brands Page 3 porn", published before he became editor, was "not probably something I would run now".

Forced to give evidence for the second time after the inquiry heard criticisms of the newspaper from a coalition of women's groups, Mohan insisted that Page 3 of the Sun was an innocent staple of British life and its daily pictures of topless models celebrate natural beauty.

• This article was amended on 11 February 2013 to include the full Twitter response from former News International chairman Les Hinton to a question about Rupert Murdoch's tweet.