Icahn: I pushed for a $150 billion buyback from Apple CEO Tim Cook

'We have a lot of options': Icahn on Apple

It looks like Apple's CEO Tim Cook is going to be hearing a lot more from Carl Icahn.

The billionaire investor said Tuesday on CNBC's "Fast Money" that the tech giant is missing a golden opportunity if it doesn't issue a bigger share buyback, and he intends to make sure that shareholders are represented even if the board does not want to go ahead with a bigger buyback.

"I feel very strongly about this," Icahn said. "I can't promise you the stock will go up and I can't promise you they will do the buyback. But I can promise you that I'm not going away until they hear a lot more from me concerning this."

Apple's board is 'not God': Icahn

Icahn said in a tweet Tuesday that he had pushed Apple CEO Tim Cook on Monday evening for a $150 billion share buyback, adding that the two would continue the discussion at another time.

"Had a cordial dinner with Tim last night. We pushed hard for a 150 billion buyback. We decided to continue dialogue in about three weeks," Icahn's tweet said.

In a CNBC interview, however, Icahn emphasized how strongly he feels about an increased buyback.

"It's a no-brainer and it makes no sense for this company with their multiple being so low not to do a major major buyback. And there's another reason that I mention, that I think might go forgotten, the fact that you can borrow money so cheaply today. I don't think we are going to see this again," Icahn said on CNBC's "Halftime Report."

"They have a golden opportunity to go borrow money."

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With Apple trading at about $482 per share, a repurchase of this kind would mean buying more than 300 million shares. Apple currently only has about 900 million shares outstanding, so a buyback of this size would be a reduction of more than than one-third.

In April, Apple announced that it would return as much as $100 billion to shareholders by the end of 2015, $60 billion of which would be through a share buyback program. It also raised its dividend 15 percent. By June, Apple had already purchased about $16 billion worth of its own stock.

While a $150 billion buyback program is well above the current buyback, Apple likely wouldn't have trouble funding an increased buyback.

As of July, Apple had $147 billion in cash and short-term and long-term securities. And even by low estimates, the tech giant is estimated to generate about $50 billion in free cash flow next year.

What's more, sales of the iPhone 5S and iPhone 5C surpassed the street's expectations, so it's likely the tech giant will just keep adding more cash to its stockpile. And it's becoming more clear that Icahn, who is believed to have a $2 billion stake in the company, wants more of that cash.

(Read more: Apple shareholders cross fingers for bigger buyback)

Icahn said in August that if Apple would issue a larger share buyback, the stock could be worth as much as $700 a share.

—By CNBC's Cadie Thompson. Follow her on Twitter @CadieThompson.