NEW YORK (CNN/Money) - Time Warner stock rallied Thursday on reports that it's holding talks with Microsoft regarding an alliance with or investment in America Online.

A source close to the situation told CNN that there have been discussions between the two companies on how to leverage the search and advertising components of the businesses. This person said it's conceivable there could be an investment down the road, but that there was no deal yet.

The New York Post, which first reported the story, said that under terms being discussed, Time Warner (up $0.59 to $18.51, Research) would be equal partners with Microsoft (down $0.01 to $26.30, Research) in a combination of AOL and Microsoft's MSN Internet unit. Microsoft would give Time Warner some cash in addition to contributing MSN to it, the report said.

Officials at Time Warner and Microsoft had no comment on the reports.

Wall Street analysts who follow Microsoft said the story in the Post was the first they had heard of the talks. They said that if a deal is struck, it could be reviewed by the Department of Justice.

Part of Microsoft's goal in the talks is to get AOL to switch to its search engine, according to a separate report in the Wall Street Journal. AOL currently uses Google's search technology, and gets 110 million site visitors a month, making it Google's single largest revenue source, according to the paper.

The Post reported that the companies are hopeful they can wrap a deal up within the next couple of months, but that Time Warner is also holding discussions with Internet search leaders Yahoo! (Research) and Google (Research) over a sale or venture with AOL in case the Microsoft negotiations fall apart.

Time Warner, the world's largest media company, was purchased by America Online, but the combined company's stock has performed badly since the January 2001 closing of the deal. CNN/Money is a unit of Time Warner.

The New York-based company is under pressure from a shareholder group led by financier Carl Icahn, who is pushing for the company to sell some units and repurchase more outstanding shares in an effort to raise stock price.

While AOL is profitable, reporting revenue of $8.6 billion and operating income of $1.1 billion in the 12 months ended June 30, it has continued to lose subscribers as customers leave its core dial-up service for high-speed Internet connections.

At the end of June, it had 20.8 million subscribers, down 2.6 million from a year earlier and down 5.7 million from three years ago. AOL is seeking to shift to a more advertising-based portal model, rather than one that depends upon subscription revenue.

Icahn has called for a sale of the company's cable unit, which Merrill Lynch estimates could fetch $40 billion, while it puts the value of AOL at only $8.8 billion.

But Mario Gabelli, whose Gabelli Asset Management owns more than 15 million shares of Time Warner, estimated at an investor conference earlier this month that if AOL's portal strategy is successful, the AOL unit could be worth $50 billion.

The pressure from Icahn increased Monday when he announced that his group, which holds a 2.6 percent stake in Time Warner, would seek seats on the company's board.

The Post also said in its report that Time Inc., Time Warner's magazine unit, could be sold in 2006 if its performance doesn't improve.

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For a look at Carl Icahn's proposals for Time Warner, click here.