Eastman Kodak Co. is preparing to seek bankruptcy protection in the coming weeks, people familiar with the matter said, a move that would cap a stunning comedown for a company that once ranked among America's corporate titans.

The 131-year-old company is still making last-ditch efforts to sell off some of its patent portfolio and could avoid Chapter 11 if it succeeds, one of the people said. But the company has started making preparations for a filing in case those efforts fail, including talking to banks about some $1 billion...