Even though Apple Inc. (NASDAQ:AAPL) had already bought back $16 billion in shares by the end of June, there’s a good chance activist investor Carl Icahn will push for even more. He is expected meet with Cook this evening to discuss the possibility of more share buybacks.

Apple Cook Icahn

Apple’s plan to buy back shares

CNBC’s Cadie Thompson notes that Apple Inc. (NASDAQ:AAPL) has been pretty active in returning money to shareholders. Bowing to pressure from hedge fund manager David Einhorn in April, the company announced a new buyback program of $60 billion, which the company said would last until the end of 2015. But while that plan announcement had a very small impact early on, shareholders have apparently remained largely unimpressed by it, if Apple’s share price is anything to go by.

Icahn tweeted that he had taken a stake in Apple Inc. (NASDAQ:AAPL) back in August and that he wanted the company to increased its share repurchasing even more. Specifically, he thinks the company should take advantage of the ultra-low interest rates to borrow money and buy back more shares.

Apple investors want more

According to CNBC, some shareholders hope Icahn gets his way. Granite Investment Advisors’ Timothy Lesko told the network that although there isn’t “a dollar figure” they would like to see Icahn press for, but they do want Apple to increase its payout ratio. Lesko notes that currently Apple’s at a 27 percent shareholder payout, but he said they would like to see the company move up to between 30 and 40 percent payout.

Speaking on Squawk on the Street, he said they would like to see Apple Inc. (NASDAQ:AAPL) “consistently increase the amount back to shareholders.” He believes that since the company is able to generate a massive $30 billion in free cash flow, “it would just be nice” for the company to sequentially keep giving it back to its shareholders.

As of this writing, shares of Apple were down 1 percent.