Apple Computer CEO Steve Jobs is reportedly in advanced talks about selling his movie operation, Pixar Animation Studios, to the Walt Disney Company, in a deal that would make him the media giant’s majority shareholder, according to Thursday’s edition of The Wall Street Journal.

Disney is clearly eager to keep Pixar on board, and that necessarily involves Mr. Jobs, who is Pixar’s chairman and CEO.

Pixar has produced a string of hit movies for Disney, such as Toy Story, Finding Nemo, and The Incredibles, featuring cutting-edge computer animation, ever since the two companies struck up a relationship more than 12 years ago.

During 2004, Mr. Jobs said he planned to end the relationship when the contract expires at the end of this year and look for another distribution partner.

He was reportedly unhappy with Disney’s former CEO, Michael Eisner. However, now that Robert Eiger has taken over as the mouse’s chief executive, the relationship has warmed up considerably.

Last year, Cupertino, California-based Apple struck a deal with Disney to feature downloads of shows from Disney’s ABC TV network, such as Desperate Housewives and Lost, in Apple’s iTunes service when Apple introduced the video version of its popular iPod device last October (see Apple Up 9% on Video iPod).

Shares of Pixar jumped $1.90 to $59.16 in recent trading, while Disney shares rose a nickel to $25.27, and shares of Apple dropped $1.57 to $80.92.

On Wednesday, Apple had warned in an earnings report that its second-quarter sales and earnings would fall short of expectations as it makes the transition to Intel-powered machines in the first quarter (see Apple Falls on Q2 Guidance).

Pixar Overvalued?

Banc of America Securities analyst Michael L. Savner believes Pixar is already trading above fair value after weeks of speculation over a deal with Disney. He puts the fair value at $44 per share.

“We think it would be difficult for Disney to justify an acquisition strategically or economically at the current price, raising questions about how much of a premium it might pay,” he wrote in a research note.

The talks with Disney may simply extend Pixar’s existing distribution deal, or Disney may opt to purchase a stake in Pixar rather than buying the entire company. Mr. Jobs is likely to end up with a seat on the Disney board under either outcome.

Pixar began when Mr. Jobs bought the computer graphics animation division of Star Wars filmmaker George Lucas’s Lucasfilm during 1986 for $10 million. He named the company Pixar and paid to produce its first short films.

He is the majority shareholder in Pixar and holds more than 60 million shares, or 50.6 percent of the company, according to the WSJ.

John Lasseter, a former Disney exec who directed Pixar’s Toy Story and its upcoming animated flick Cars, is likely to become the head of Disney animated movies if the deal goes through.