"Tmrw we'll be sending an open letter to @tim_cook. Believe it will be interesting," he tweeted through his handle @Carl_C_Icahn.
The investor has in the past urged Apple to return more of its cash to shareholders and pressured the company to raise its stock buyback and dividend.
Icahn also tweeted that his fund had announced a large position in Apple just over a year earlier and noted that the company's stock had risen 50.6 percent since then.
Icahn was not immediately available for comment.
Apple shares were up 2 percent at $100.73 in late afternoon trading. More than 43 million shares had changed hands by 15:11 p.m. ET.
"This story is developing."
© Thomson Reuters 2014