Apple Inc. is working with component suppliers in Asia to test a new tablet computer with a smaller screen, people familiar with the situation said, as it looks to broaden its product pipeline amid intensifying competition and maintain its dominant market share.

Officials at some of Apple's suppliers, who declined to be named, said the Cupertino, Calif., company has shown them screen designs for a new device with a screen size of around eight inches and said the company is qualifying suppliers for it. Apple's latest tablet,...