McLane, when reached by MLB.com on Friday, wouldn't confirm the report.
"We're negotiating with him, but we're negotiating with several other people," he said. "We're trying to do a deal with several people, and certain Jim Crane is one of them."
McLane announced in November he was accepting offers for the sale of the club he purchased more than 18 years ago, and he said he desired local ownership. Crane is the CEO and founder of Houston-based Crane Capital Group.
McLane said in December 2009 that he had a tentative agreement with Crane to purchase the Astros following the 2008 season, but a deal couldn't be reached. Crane previously bid to purchase the Chicago Cubs and Texas Rangers.
The negotiations are being handled by Steve Greenberg of Allen & Company, a New York-based investment bank. Greenberg said in March he was in discussions with multiple parties and that the process was "closer to the finish line than we are the starting line," but didn't acknowledge Crane's interest.