So why isn't there more app store competition?
If you want to download an app on your phone, you'll most likely head to a marketplace owned by Apple or Google. It'll be tough for any wireless carrier to establish an alternative.
When consumers want to download applications on their smartphones and tablets, it's usually Google or Apple that's assigned the role of gatekeeper.
But is that the way it has to be?
A spokesperson for the carrier told CNET it has "no plans" to build a store, though The Information is standing by its report.
Regardless of what Verizon does, the potential for app store competition raises questions about who could meaningfully take on Google or Apple in their dominance over app marketplaces. Google and Apple did not respond to requests for comment.
App stores are a huge element of the modern mobile technology market. They suggest what apps people should install, extract up to 30 percent of sales, and store credit-card data that makes it easier to persuade millions of users to expand from apps to other domains like music or books. But it's hard to get customers who are accustomed to one sales channel to move to another, and it's hard to coax developers to submit their apps to multiple app stores.
The app-discovery business is increasingly attractive as consumers continue to shift away from desktop computers to phones and tablets. With the migration, browsing the web with a general-purpose browser has become less common as people embrace apps tailored to specific functions. Both Apple's and Google's stores have more than a million apps each.
There are, of course, other app stores. Amazon and Microsoft have their own storefronts. And there are smaller services like Xyo or Quixey that aim to streamline app discovery. But there are no go-to alternatives to the two tech-giants.
For carriers to try to fill that role is an interesting prospect. They've tried it before. In 2010, several carriers -- including Verizon -- launched an initiative called the Wholesale Applications Community, which tried to establish a global app store. They shuttered the effort last year.
But according to The Information's report, a carrier could leverage its position to lure people away from Google's and Apple's stores. For example, it could grant apps in its own store a network speed advantage or discount the cost of data used by apps.
Wireless-industry app stores would indicate an ambition to reclaim lost influence over the mobile software people use. But getting customers enthusiastic about carrier app stores would be tough.
"It would require a significant change in consumer habit," said Sameet Sinha, an analyst at the investment bank B. Riley and Co. He added that customers used to have to download games directly from carriers, but that they've been less dependent on wireless companies for content over the past several years, after the iPhone soared in popularity.
One way challengers could differentiate app stores to attract customers, as noted by The Information, would be a more interactive experience than Google's Play store. The marketplace could use contextual algorithms to push app suggestions to consumers based on what they're doing at the moment. For example, at breakfast the store could surface a finance app to go with your morning coffee, or travel apps if you're in a car. That strategy is Google's core skill: using data to personalize experiences. The search giant has invested heavily in its own predictive service Google Now -- and there's no reason Google can't integrate that functionality into its own app store.
"For Google, it just means they need to offer more of those tools," said Sinha. "Google needs to be that starting point. There's no reason they should lose out on that."
The carriers' challenge is similar to that of other companies vying to increase their presence on mobile devices, jostling for space on platforms owned by Google and Apple. Because Apple closes off its software to modifications from outside firms, companies have focused on Android -- which powers 80 percent of the world's smartphones -- to gain ground. In January, Yahoo bought the startup Aviate, which takes over an Android phone's home screen to surface relevant content and app suggestions, akin to what Verizon reportedly intends to do. In April, Twitter bought a company called Cover that works similarly.
Carriers' motivation could also stem from Google's decision to slightly reduce over the past year the revenue it shares with carriers and hardware partners, from 25 percent to 15 percent in most cases. Seventy percent of the revenue goes to the developers who make the apps. Google made $2 billion on its app store, before divvying it up between carriers and handset makers, according to the report.
For Google, its Play store is an important business, though just a drop in the bucket for the company, which is projected to make $67 billion this year. Originally called the Android Market, the Play store was announced in 2008. Downloads from the store exceeded those from Apple's iOS App Store by around 60 percent in the second quarter, according to mobile analytics firm App Annie. The firm also said, however, that Apple's App Store still earned about 80 percent more in revenue.
In Google's most recent earnings report, "other revenue," which includes Google Play sales, accounted for 10 percent of total revenues. The figure rose 53 percent from last year to $1.6 billion.
The company has big hopes for Google Play, as it tries to expand Android to dominate more than just smartphones, but also everything from smartwatches to televisions to car dashboards. The Play store could be the place where people get all their entertainment, and it could be the seamless content library that ties all those disparate Android-powered devices together, said Sinha.
"Google has an opportunity to take a piece of that," Sinha said, "and maintain their control over it."