The companies are discussing a deal that could be unveiled as soon as Monday, The Wall Street Journal reported, citing people familiar with the matter.
The transaction's specific details, including exactly what SK Hynix would be acquiring, could not be learned, the paper said.
Shares of the Santa Clara, Calif., company at last check were up 1.7% to $55.08.
The Intel unit makes NAND flash-memory products primarily used in devices such as hard drives, thumb drives and cameras.
Intel has been weighing getting out of the business for some time, driven by sagging prices for flash memory, the Journal reported.
Intel is scheduled to report its third-quarter earnings Thursday afternoon.
The market for memory chips slumped in 2018 amid an oversupply of the devices, though it began to recover late last year, the paper reported. Analysts expect the market for NAND devices to remain strong in the coming years as data storage surges.
Intel's market value is roughly $230 billion. The company's stock is down about 10% this year, compared with a roughly 30% rise in the PHLX Semiconductor index.
While Intel has struggled to move into mass production of its most advanced chips, rival Advanced Micro Devices' (AMD) - Get Report market share in personal computer CPUs climbed above 17% in the first quarter, more than doubling from five years earlier, the Journal said, citing Mercury Research.