Apple is working on a strategy to expand the iPhone’s market share, according to research notes released yesterday from Bernstein Research analyst Toni Sacconaghi, which were covered by Forbes. Sacconaghi met with Apple execs last week, including Apple COO Tim Cook, CFO Peter Oppenheimer and vice president Eddy Cue.

While none of the executives said specifically that Apple would be introducing a smaller or cheaper iPhone, Sacconaghi said that Cook admitted the company is working on some “clever things” to address the prepaid market, adding that Apple doesn’t want its products to be “just for the rich.”

Adding to his comments about expanding to the prepaid market, Cook noted that the company has spent “huge energy” in China, which he called a “classic prepaid market.”

While Oppenheimer didn’t name names, he did say that getting the iPhone to more carriers is a must. According to Sacconaghi’s notes, Apple currently touches only 175 carriers, versus the more than 550 that Research In Motion supports.

Sacconaghi’s notes seem to be in keeping with last month’s New York Times report, which shot down rumors that Apple was looking to shrink the iPhone’s form factor to create an iPhone “Nano.” The New York Times report did, however, note that Apple was looking to bring down component prices, which would result in a lower retail price.

IHS iSuppli recently published notes that concluded Apple has committed $3.9 billion to secure production of the company’s retina displays. Oppenheimer told Sacconaghi that Apple would likely continue to form partnerships to secure supplies of key components.