NEW YORK (CNN/Money) - AOL chief executive Jonathan Miller tried to convince Time Warner directors Thursday that the world's biggest Internet service provider is still a growth business, and the board's response was "engaged" and "fairly positive," according to a person familiar with the situation.

Miller's presentation to the Time Warner board lasted about an hour Thursday morning.

Analysts have said Miller needs to convince Time Warner (TWX: up $0.20 to $16.99, Research, Estimates) that the AOL unit is worth keeping despite the sharp drop last year in subscribers for its dial-up online service.

Miller's strategic plan calls for AOL to make some of its content available free to non-AOL subscribers so that it can pull in more visitors to its Web site in a bid to boost ad revenue, the source said.

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AOL lost more than 3 million subscribers last year to its dial-up service, but Miller is expected to say that AOL can manage that decline by growing its advertising, broadband and international businesses.

AOL's higher-priced broadband service added 1.8 million subscribers last year.

Miller, 47, who previously worked for hard-charging Barry Diller at USA Networks, joined AOL in late 2002 with a mandate to resuscitate the business.

In 2003, AOL created a separate, lower-priced service that offered more videos and music, but which required subscribers to already have a high-speed Internet connection.

Time Warner is the parent of CNN/Money.