YouTube is seeking streaming rights to TV series and movies to bolster its new subscription service, intensifying its rivalry with Netflix Inc., Amazon.com Inc. and Hulu in the competitive market for online video.

Executives of YouTube, the Alphabet Inc. unit that is the world’s largest online-video service by viewers, have met with Hollywood studios and other production companies in recent months to consider pitches and negotiate licenses for new content, according to people familiar with the situation.

Susanne...