Speaking to The Huffington Post UK, activists from the 'No More Page 3' group - who have petitioned for the newspaper to drop its "sexist" images of topless women - said they were "encouraged" by the messages from the world's most powerful media mogul.
Before acknowledging that the Sun's long-running feature was "old-fashioned," Murdoch provoked a flurry of mixed responses on Twitter this morning after asking his 520,0000 followers if they thought Britain's top-selling newspaper should still feature topless women in every edition.
Lucy Holmes, the leading force behind the campaign to end Page 3, told Huff Post UK that the tweets from the News Corp boss showed that Murdoch was finally paying attention to those opposed to the feature, which has appeared on the newspaper's pages for more than 40 years.
"What is really encouraging is that Rupert Murdoch's tweets this morning certainly show that he's reconsidering the future of Page 3," she said.
"We're not going lie though, it's unfortunate that he misses the point entirely by asking a question about whether young women are more attractive clothed or unclothed. (Sigh)."
The Sun told Huff Post UK that the paper remained "committed to listening to our readers."
"While all aspects of The Sun are continually under review, we remain committed to listening to our readers and producing the newspaper that they want to read," a spokesperson said.
Murdoch provoked a further Twitter furore after following up on his initial tweet by saying that British feminists "bang on forever about page 3."
But Ms Holmes said the campaign group is "really encouraged that change is afoot."
"Brit feminists banging on about Page 3 have made Murdoch and the Sun realise that the rest of the country isn't down with their 1970s sexism," she said.
However, last year Sun editor David Dinsmore told the BBC the paper will continue to print pictures of Page 3 girls because it is what readers want.
He told BBC Radio 5 live's Breakfast, "I was flicking through a copy of this month's Vogue and there was a picture of Kate Moss topless. I suspect the editor of Vogue won't be questioned on whether topless pictures should be around on its pages," he said.
Murdoch hinted in February last year that the topless women may be replaced with a "halfway house" of "glamorous fashionistas".
Responding to a tweet which said: "Seriously, we are all so over page 3 - it is so last century!" Murdoch replied: "You maybe [sic] right, don't know but considering."