A report from Bloomberg cited people said to be familiar with the move, as saying the plan, known internally as Kalamata, was still in the early stages of development.
It was said to be part of a bigger move to make all the company's devices — iPads, iPhones and Mac computers — work together better and had been approved by company executives.
A report in October last year said Apple had designed iPhones and iPads that would not use chips designed by Qualcomm, a company with which Apple has legal disputes ongoing.
The Bloomberg report said Intel shares had fallen by about 9.2% on the news. Intel gets about 5% of its annual revenue by supplying chips to Apple.
The main processors for iPhones, iPads, Apple Watches and Apple TVs are made by the company itself and based on designs from ARM.
The move to its own chips is expected to see the use of a new software platform that would allow users to run iPhone and iPad applications on Macs.
Apple and Qualcomm have been on the warpath since January last year when Apple filed a suit against Qualcomm in the US, followed by two cases in China the same month. Two months later it filed a case in the UK.