Apple Inc., locked in an intensifying legal fight with Qualcomm Inc., is designing iPhones and iPads for next year that would jettison the chipmaker’s components, according to people familiar with the matter.

Apple is considering building the devices only with modem chips from Intel Corp. and possibly MediaTek Inc. because San Diego, Calif.-based Qualcomm has withheld software critical to testing its chips in iPhone and iPad prototypes, according to one of the people.

Qualcomm,...