According to a person familiar with the matter, the studio is negotiating to pay about $1 million for the rights to the project.
The person declined to be identified because the deal has not been finalized.
Sony was also behind the Oscar-winning biopic "The Social Network," about Facebook founder Mark Zuckerberg, and "This Is It," a documentary made of concert rehearsal footage of pop star Michael Jackson.
The news was earlier reported by Hollywood blog Deadline.com.
After Jobs' death on Wednesday, publisher Simon & Schuster pushed up the release date on Isaacson's "Steve Jobs" by a month to Oct. 24.
Large numbers of pre-orders of the digital e-book for $16.99 pushed the title to No. 1 on Apple's iTunes store and No. 2 on Amazon.com. Pre-orders of the hard cover copy, for $17.88, put the book at No. 1 on Amazon.