Apple CEO Tim Cook is expected to meet with billionaire investor Carl Icahn on Monday, and it's widely speculated that Icahn may push for a bigger buyback.
During the last 18 months Apple has been active when it comes to returning cash to shareholders. In April, the company announced a massive stock buyback program of $60 billion before the end of 2015 and by June Apple had already bought $16 billion worth of its stock.
(Read more: Carl Icahn buys more Apple; calls it a 'no-brainer')
But Apple's move to increase shareholder value didn't seem to satisfy investors. Rather, based on its stock performance they appear to have an appetite for even larger returns, which is where Icahn comes in.
Icahn, who has taken a large stake in Apple, posted a tweet in August about pushing Apple to increase its stock buyback. He also said that Cook was on board with the idea and mentioned a planned September dinner with Cook to discuss the matter. The get-together is expected to happen in New York on Monday evening.
Some Apple shareholders are hoping Icahn will get his way.
"I can't say there is a dollar figure we want him to press for," said Timothy Lesko of Granite Investment Advisors, which has owned Apple shares for over a decade. "We would like to see them increase the payout ratio. Right now, it's at about a 27 percent payout to shareholders, and perhaps they can move up to a maybe 30 to 40 percent payout to shareholders."
While Lesko said he is happy to see Apple, under Cook's leadership, dramatically increase its payout to shareholders, there is still room for even more value to be returned.
"As we continue to see Apple deliver on its promise furthering out the iOS infrastructure and developing new products, we would just like to see it consistently increase the amount back to shareholders," Lesko said on CNBC's "Squawk on the Street."
"If they are going to generate $30 billion in free cash flow, it would just be nice to see, on a sequential basis, them to continue to give that back to shareholders."
—By CNBC's Cadie Thompson. Follow her on Twitter @CadieThompson.