Details on the alleged meeting plans were revealed on Thursday by CNBC, which said the two will also "discuss the company's prospects." Icahn is believed to currently hold about $2 billion worth of AAPL stock.
Icahn has publicly pushed for Apple to buy back more shares in itself. Via his official Twitter account, he revealed that he would meet with Cook for dinner sometime in September.
Icahn has said he believes that shares of AAPL are "extremely undervalued" at their current price. His support of the company helped to push Apple past $500 per share last week, though the stock price fell back below that threshold in subsequent weeks.
Apple spent $16 billion last quarter alone on repurchasing 36 million in shares. The original schedule had called for the company to buy 10 million in shares in the third quarter, but Apple apparently decided to push harder and buy at an average share price of $444.44 ? more than $250 off from the company's high of $702.10 reached last September.