According to people familiar with the matter, fewer than 10,000 people are using CNN+ on a daily basis.
The people spoke with CNBC in order to discuss non-public data.
CNN+ was launched on March 29. The news streaming service, which costs $5.99 a month or $59.99 annually, is only available on the Roku platform. The recent combination of Discovery and WarnerMedia into Warner Bros. Discovery casts doubt on the future of the application.
CNN's cable network still rang up an average of 773,000 total viewers a day despite a sharp decline in viewers last year.
After only two weeks, CNN is happy with the launch and progress.
CNN sought to make a huge splash with CNN+, attracting big-name talent from rival news networks, such as Chris Wallace from Fox News. As entertainment-first options dominate the landscape, there is skepticism whether there is enough demand to sustain a news streaming service. Disney+ had more than 10 million subscribers on its first day of existence.
CNN has not released an exact number of CNN+ subscribers. 21.3 million people have signed up for Disney's ESPN+, which offers sports news programming in addition to live event broadcasts. NBCUniversal's Peacock, which features news programming, has more than 24 million active accounts in the US, with 9 million of them being paid members. Peacock offers premium tiers starting at $4.99 a month, while the Disney channel charges $6.99 a month.
David Zaslav hasn't commented on CNN's long term future. He told CNBC that he would need to see how the application performed before making a decision.
I haven't gotten a business review on what CNN+ is going to be and how it will be offered, Zaslav said at the time.
People familiar with the matter say it is possible that CNN+ programming will be part of a larger bundle. There are millions of subscribers to those services.
The ex-WarnerMedia CEO decided to launch CNN+ two weeks before merging the company with Discovery. Kilar left the company last week. He told CNBC that subscriber numbers were ahead of his expectations, but he wouldn't say what that meant.
It is ahead of my expectations in terms of where the subscribers are, the engagement, and the receptiveness that we are getting in terms of people.
The new leadership at Warner Bros. Discovery plans to cut hundreds of millions of investment dollars for the service given concern over its future. Chris Licht will join Warner Bros. Discovery on May 1 and will make decisions on how best to proceed, two people said.
NBCUniversal is the parent company of CNBC.