This reporting comes from Bloomberg's Mark Gurman, he in particular seems to have the pulse on the inner workings at Apple. The program has been underway using the codename Marzipan, and would see apps originally designed for the iPhone and iPad make their way to macOS devices.
According to the report, Apple will initially only allow iPad app developers to port their apps over to Macs thanks to a new SDK. It's expected that Apple will announce this initiative at this year's Worldwide Developer Conferences (WWDC). "Developers will still need to submit separate versions of the app to Apple’s iOS and Mac App Stores," writes Gurman. "But the new kit will mean they don’t have to write the underlying software code twice, said the people familiar with the plan."
Porting iPad apps to macOS seems like it would make the most sense given the expanded display real estate afforded by the iPad/iPad mini/iPad Pro form-factors. However, developers will also be able to port over their iPhone apps; that next phase in Apple's Marzipan roadmap is said to kick off in 2020 (likely at WWDC 2020). Finally, the universal apps would be available to the public the following year, that is if everything goes according to schedule.
So, what’s the end game? Much like Microsoft’s Universal Windows Platform (UWP) for Windows 10-based hardware, developers will eventually be able to create apps with a single binary that would work across all of Apple's major computing hardware platforms: iPhone, iPad and Mac. While Apple has not yet given developers the tools to create these cross-platform apps, the company's software engineers have already showed what's possible last year when it introduced macOS Mojave. Mojave saw the introduction of long-standing iOS apps like Stocks, Voice Memos and Home make their way to macOS.
In the end, this move will make it easier on developers that want to bring their apps to as many of Apple's platforms as possible without expending too many resources. It would also allow for Apple to add some more spice to the macOS App Store which is not nearly as "well stocked" with compelling apps as its iOS App Store counterpart.
It should also be noted that this move to universal apps should help in Apple's rumored plan to kick Intel to the curb as a supplier of CPUs as it shifts to its own hometown ARM-based processors for Mac desktops and MacBook laptops.