The Cupertino, California, company aims to top $50 billion in annual services revenue by 2021, and a magazine subscription service would likely contribute to that.
He didn't say exactly how Texture would be rolled into Apple News.
The "virtual newsstand" gives readers online access to current and back issues of about 200 titles, including Rolling Stone, Vanity Fair, Vogue and Cosmopolitan, for a monthly fee of $9.99 (£7.19).
Apple SVP of Internet Software and Services Eddie Cue appeared on stage at SXSW on Monday, and discussed a range of topics, including their just-announced acquisition of magazine app Texture.
Apple made its first big push to integrate magazines and newspapers into its devices with an application called Newsstand in 2011.
While Cue said Apple won't be purchasing Netflix (it could if it wanted: Apple is worth over $910bn and Netflix is $25bn in debt), the tech giant recently hired two executives for its grand TV strategy and now has a team of 40 people both based in the USA and overseas.
Today Apple revealed that it is to acquire the digital magazine subscription service Texture. Texture's apps for iOS, Android, and Windows 10/8 (yes) will continue to work - at least for the time being.
The largely evasive talk, titled "Curation in Media - Why It Matters", took the Austin Convention Centre audience through Apple TV and News strategy. "We could not imagine a better home or future for the service".
And yet, CNN's Dylan Byers, who interviewed Cue, asked why the NRA has a presence in the App Store and on Apple TV.