As Apple Inc. prepares to unveil both a new high-end iPhone and a cheaper version for the first time next week, it is already working on something bigger.

The electronics giant has begun evaluating a plan to offer iPhones with screens ranging from 4.8 inches to as high as 6 inches, people familiar with the matter say. That would be a sizable leap from the 4-inch screen of the iPhone 5 released last year, and, at the upper end, would be one of the largest on the market.

Such plans signal further that the Cupertino, Calif., company is shifting its smartphone strategy as it searches for new engines of growth, and as competition with Samsung Electronics Co. intensifies.

The Korean rival has taken a commanding lead in smartphone market share in part by offering an array of devices at different prices and sizes. On Wednesday, Samsung unveiled the Galaxy Note 3 with a screen measuring 5.7 inches, a size that places the device in a category of hybrid phone-tablets.

It is unclear whether Apple will ultimately choose to follow a multi-size, multi-device strategy beyond shipping a new lower-cost model for the first time later this month. The company often tests different devices and configurations before choosing a course.