At US $216 per share, Apple - already the world's most valuable company - would be worth about US $1.3 trillion, or about the size of South Korea's gross domestic product.
The company is valued at just over US $700 billion currently.
Icahn, one of Apple's top 10 investors, has long urged the company to buy back more shares and raise its dividend.
The activist investor said in October that Apple shares could double in value and urged the board to buy back more shares using its cash pile. At the time, the shares were trading at $100.
"... We look forward to the capital return program update in April, anticipating it will include a large increase to share repurchases," Icahn wrote.
Icahn said Apple shares should be trading at 20 times earnings per share, which taken together with net cash of $22 per share works out to US $216 per share.
"This is why we continue to own approximately 53 million shares worth US $6.5 billion, and why we have not sold a single share," Icahn said in a letter to his Twitter followers.
"Also, to the extent Apple introduces a TV in FY 2016 or FY 2017, we believe this 20X multiple is conservative," he wrote.
Apple had cash reserves of about $178 billion as of December 27, enough to buy IBM or the equivalent of US $556 for every American.
Apple said in April 2014 that it would return more than US $130 billion to shareholders by the end of 2015.
According to StarMine's intrinsic valuation model, Apple should be trading at US $140.90. That implies a compounded annual earnings growth rate of 9.9 per cent over the next 10 years.
Apple shares closed 2.3 per cent higher at US $124.88 on the Nasdaq on Wednesday. Up to Tuesday's close, the stock had gained more than 22 per cent since October 9.