A deal could be announced within a week, The Wall Street Journal reported, citing unnamed sources.
Intel had moved to exit the modem business in April, after Apple and Qualcomm (QCOM) - Get Report settled a long-running patent dispute. The settlement meant that Apple would shift away from sourcing modem chips from Intel under a multi-year deal with Qualcomm.
Modem chips are likely to see expanded use in internet of things applications as more and more devices are hooked up to the internet.
Shares of Apple rose 28 cents to $207.50 in after-hours trading Monday after gaining 2.3% in the regular session.
Intel rose 67 cents to $52.02 in after-hours trading.
Qualcomm fell $1.67, or 2.2%, to $74.28 in after-hours trading.