Billionaire Carl Icahn teases letter to Apple CEO Tim Cook to promote new website

Icahn took to Twitter to promote his new website, and also to tease that the letter to Cook will be published on "Shareholders' Square Table" when it launches on Thursday. As of Wednesday, the site simply advertises that it is coming soon.

The investor declined to reveal anything about the contents of his letter to Cook, but an unnamed source revealed to CNBC that the note is part of Icahn's continuing efforts to persuade Apple to initiate a larger buyback of its own shares. In return for accepting his pitch, Icahn has reportedly offered an "unknown pledge."

Apple already has a plan underway in which it will spend a total of $100 billion through 2015 on share buybacks as well as dividend payouts. But Icahn believes Apple should increase its share buyback program and spend $150 billion on its own shares.

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.

But Icahn's reputation on Wall Street gives him considerable sway — enough to land him a private dinner with Cook and Apple Chief Financial Officer Peter Oppenheimer in New York last month. Talks between the three men reportedly became "a little testy" at times, though Icahn also characterized the meeting as "cordial."

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.