Speculation swirled late last year that Apple (AAPL) could be considering a switch away from Intel chips in its notebook computer lines, opting instead to use its own in-house ARM-based chipsets. Such a move likely wouldn’t happen anytime soon, but Intel (INTC) may have found a way to benefit from this eventual shift away from its processors while actually boosting its business with Apple in the process: Build Apple’s in-house chips.

According to a report from Reuters, gaining Apple’s chip business will be a top priority for Intel’s next CEO and negotiations are already underway. The site’s sources claim that executives from both companies have discussed the possible partnership over the past year, but no deal has been reached at this point.

The move could improve the quality of Apple’s mobile chips thanks to Intel’s leading process technology, and an added benefit for Apple would be to finally sever all ties with rival Samsung (005930), which continues to supply components for various Apple devices.

“After Intel upped its capital spending budget by $2 billion to $13 billion this year, speculation grew that Apple could ink a deal to use Intel’s leading process technology to make better chips for its iPad and iPhone,” Reuters’ Noel Randewich and Nadia Damouni wrote in the report. “Doing so could help Apple end its foundry relationship with Samsung, which has become a fierce competitor with its own smartphones and tablets.”

The report also notes that Sunit Rikhi, VP and general manager of Intel’s foundry business, said last week that his group is ready to begin building chipsets for a potential large mobile customer, but he declined to clarify whether or not that customer might be Apple.