The report, citing two industry executives with knowledge of recent discussions between the companies, said Apple will agree to use Intel chips.
Neither company would confirm the report and an Apple spokeswoman told the Journal she would characterize it as "rumor and speculation."
It was unclear whether such a move would signal a large-scale shift away from chips made by IBM (IBM), Apple's longtime supplier, the report said.
Apple could choose to add some Intel-based models to its product line or make a complete shift to Intel's chip technology in what would be seen as a serious blow to IBM's microprocessor business, the newspaper said.
Adopting Intel chips would help ensure that future Macintosh systems could meet the price and performance of products from tough rivals such as Dell Inc. (DELL).
Apple's pricing, which has often been higher than rivals, could become more competitive if Intel provides the kind of marketing subsidies it has given to other computer makers, the newspaper said.
Apple sells only about three million computers a year -- a small portion of the estimated 200 million sold globally.
But for Intel, winning over Apple would be a prestigious endorsement from one of technology's most influential trend-setters and could associate the chipmaker with Apple's hugely popular iPod music player.
Apple's shares have nearly quadrupled since the iPod was introduced in October 2001.