The health of Apple's chief executive is set to top the agenda at the company's annual general meeting, later today.
A group of shareholders is calling on the firm to make public its management succession plan.
Apple's charismatic founder, Steve Jobs, is currently on his third medical leave of absence since being diagnosed with pancreatic cancer in 2004.
Meanwhile, the company is being run by chief operating officer, Tim Cook.
Although shareholders are sympathetic to Mr Jobs' ill health, some are pressing for greater clarity about Apple's future leadership.
Those calls are being led by the Central Laborers' Pension Fund, of Jackson, Illinois.
It holds nearly 11,500 Apple shares, worth around $4 million (�2.4m).
The fund wants Apple to name possible long-term successors, something the company is unwilling to do.
Visionary leaderSuch is Mr Jobs reputation as a hand-on, visionary leader, that his prolonged absence from the Cupertino headquarters is seen as potentially damaging.
"Given recent rumours about his poor health, the pressure is increasing on Apple to reassure shareholders and industry watchers that there is a future beyond Steve Jobs," said Gartner analyst Carolina Milanesa.
However, she dismissed the notion that his continued absence meant Apple would lose its way.
"There is more to Apple than Steve Jobs," she said.
Despite his absence, Mr jobs has been spotted visiting the Apple campus since January.
He also attended a recent dinner for technology leaders, hosted by US President Barack Obama.