AT&T Inc.’s WarnerMedia is discussing plans to package HBO, sister channel Cinemax and its vast Warner Bros. TV and movie library into a streaming service costing between $16 and $17 a month, according to people familiar with the matter, a strategy aimed at keeping the media giant competitive against lower-priced offerings in a crowded field.

The new streaming service, which will debut in “beta” form later this year, essentially includes all of WarnerMedia’s entertainment offerings and will feature its own new, original content....