Icahn also revealed in an interview on CNBC that Cook was joined by Apple Chief Financial Officer Peter Oppenheimer for their discussions in New York City on Monday. It was there that the three apparently disputed whether shareholders should have a say in how Apple executives opt to spend the company's cash.
"The board is not God," Icahn said. "And the board, in this kind of a case, should be listening to what the shareholders want."
The billionaire investor believes Apple should increase its share buyback program and spend $150 billion on its own shares. Apple's current plan calls for it to spend a total of $100 billion through 2015 on share buybacks as well as dividend payouts.
Earlier Tuesday, Icahn took to Twitter to say that he had a "cordial dinner" with Cook. The two parties will meet to continue their "dialogue" in about three weeks, which is about the same time that Apple is expected to report its fourth-quarter earnings for fiscal 2013.
Though he has publicly said he believes shares of AAPL are "extremely undervalued," Icahn has a reputation for causing trouble with tech companies. He famously opposed Michael Dell's efforts to take PC maker Dell private, won three seats on Yahoo's Board of Directors, and is also credited with helping to force out the CEO of Motorola before the handset maker was bought by Google.
Icahn is said to have about a $1.5 billion stake in Apple. While that's a considerable sum, it would not put him among the company's largest shareholders, particularly institutional investors with significant stakes.