Some of the most important investors in the country have claimed that that Apple Inc could be the first company to reach a market capitalization of $1 trillion.

Apple Inc. (NASDAQ:AAPL) is already the world’s largest publicly traded company, with a market capitalization of around $670 billion, according to Thomson Reuters data. Microsoft Corporation (NASDAQ:MSFT) is in second place with a capitalization of around $409 billion.

Apple: Backing from the big dogs

Steve Einhorn, a top executive at Omega Advisors Inc., called Apple “an attractively priced, double-digit returner” during the Reuters Global Investment Outlook Summit in New York. He also predicted that the company could “eventually” reach the trillion-dollar milestone.

Billionaire activist investor Carl Icahn was another who spoke out on his hopes for Apple Inc. (NASDAQ:AAPL). Just last month he claimed that the company should use its $133 billion in cash reserves to buy back stock. He maintains that the company is undervalued.

On Monday he claimed: “Apple Inc. (NASDAQ:AAPL) is one of the best companies I would say of the last few decades.” He claims that market undervaluation of the company and its vast cash reserves mean that “it’s like a no-brainer to buy your own stock back.”

A regulatory filing from last week showed that Icahn owned around 53 million shares in Apple Inc. (NASDAQ: AAPL ) at the end of last quarter. He refused to give what he thought was a fair price for Apple shares, claiming that it is “a question that is extremely hard to answer.”

Michael Corcelli of Miami-based Alexander Alternative Capital was more bullish on the company’s prospects of reaching the $1 trillion mark. “Absolutely, without a doubt,” he said. He reasoned that sales of the company’s already popular phones and tablets would spike over the holiday shopping period period.

“Right now Apple Inc. (NASDAQ:AAPL) is the most obvious thing that has to go up,” Corcelli continued.

Word on the Street

Most analysts are painting a more cautious picture of Apple Inc. (NASDAQ:AAPL)’s future. The average 18-month analyst target is $117 share, which would value the company at $686 billion. In order to break the $1 trillion barrier, prices would need to reach $167 per share.

Before you react incredulously to the idea of the stock rising 46% from its current price, remember that the stock has jumped 40% over this past year, largely due to strong sales of the iPhone.

Could the company break more records, or will we see another collapse of a stock market giant like during the dot-com boom?