NEW YORK — After selling millions of Americans their mobile phones, Verizon now wants to capture their eyeballs, too.

As its phone business slows down, the nation’s largest wireless carrier is making a $4.4 billion bet that it can find growth in mobile video and advertising by buying AOL, one of the Internet’s oldest brands, which has been through its own share of transformations since introducing much of America to the online world nearly a generation ago.

The acquisition is the latest effort by a wireless company to tap into some of the money shifting to streaming video and mobile devices.

Ken Doctor, a media analyst for consulting company Outsell, said Verizon is becoming less of a utility that merely provides access to online services and more of a player in the digital arena as it sees growth in the likes of Apple, Google and Facebook.

“They’re trying to move into that league of players getting money from digital, both from consumers and advertisers,” Doctor said.

For consumers, the deal could mean more advertising — and ad targeting — from Verizon. That might mean more personalized ads in online videos and AOL content that appears on Verizon handsets and in marketing messages to customers.

AT&T has taken a different tack. Last year, the company said it would buy satellite TV provider DirecTV for $48.5 billion so it could offer bundles of TV, Internet and phone services — just like cable companies. In many cases, the Internet component would be through wireless rather than fixed-wire broadband.

With the AOL acquisition, Verizon will gain access to advanced advertising technology, including the “One by AOL” platform that lets customers buy ads across platforms, including video, online and TV.