Rupert Murdoch says The Sun is "considering" scrapping the photographs of topless women it prints on page 3.
In a tweet , the chief executive of News Corporation, which owns the company that publishes the newspaper, said campaigners may be correct in describing the feature as "so last century".
He hinted to his 400,000 followers that it could be replaced with a "halfway house" featuring "glamorous fashionistas".
Mr Murdoch was replying to a tweet from Karen Mason , who managed to attract the attention of the media mogul with only her 14th post.
She wrote: "@rupertmurdoch #nomorepage3 Seriously, we are all so over Page 3 - it is so last century!"
A spokesman for campaign group No More Page 3 said: "We're really pleased that Rupert Murdoch might be thinking of dropping Page 3. It's down to everyone who signed the petition and supported the campaign.
"We won't stop until Page 3 is finally, permanently, out of the paper but his tweet is encouraging."
Within hours of Mr Murdoch posting his message, Twitter was awash with suggestions for what could replace Page 3.
One user said the page should be dedicated to "young sports stars, musicians, carers, people who hold their communities together, volunteers, rescuers", while another said : "Replace with a good news page. Uplifting and inspiring stories from all over Britain. A nice way to start the day."
No More Page 3, which has previously campaigned outside News International's headquarters in Wapping, London, has seen more than 60,000 people sign its online petition , demanding an end to Page 3.