Tesla Inc. is developing support for Apple Inc.’s CarPlay system in its vehicles, according to people with knowledge of the matter, working to add one of the most highly requested features by customers.

The carmaker has started testing the capability internally, according to the people, who asked not to be identified because the effort is still private. The CarPlay platform — long supported by other automakers — shows users a version of the iPhone’s software that’s optimized for vehicle infotainment systems. It’s considered a must-have option by many drivers.