Sony supplies nearly all of the CMOS (complementary metal-oxide semiconductor) sensors for the current iPhone 5S's rear-mounted main cameras.
Apple could be looking to switch to Sony sensors for the secondary camera on the front, which currently uses parts from suppliers in the United States and elsewhere, the business daily said.
With more customers expected to use smartphones for video calls, Apple sounded out Sony about supplying more sensors, Nikkei said.
Sony held the largest share of the global CMOS sensor market in 2012 at 32.1 percent, according to Techno Systems Research.
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Sony has laid the groundwork for stepping up production to keep up with the increase in orders, Nikkei reported.
A request from Apple was the reason for its January decision to purchase a plant from Japanese chipmaker Renesas Electronics, according to a source involved in the negotiations, the newspaper said.
Sony also supplies to Samsung Electronics, the world's No. 1 smartphone seller, and Huawei Technologies.