Netflix Inc. may soon have to contemplate life without its No. 1 show. It’s “The Office.”

NBCUniversal, which owns the show, licensed reruns of the comedy to the streaming-video giant years ago. Now NBCUniversal is launching its own streaming service, and has begun internal discussions about removing “The Office” from Netflix when the contract expires in 2021, according to people familiar with the situation.

This is about to become a recurring headache for Netflix.

Three of its biggest programming suppliers—AT&T Inc.’s WarnerMedia and Walt Disney Co. in addition to Comcast Corp.’s NBCUniversal—are entering the streaming-video arena. After licensing content to Netflix for years, happy to cash its checks, they are looking to take their hit content back to feed their own platforms.

Netflix has an air of invincibility in the entertainment world, with a huge audience, a hefty war chest and a sizzling stock. But the moves by its Hollywood rivals are a gathering threat, raising the prospect the service could lose some of its most-watched programming or have to pay a steep price to keep it.