The Palm Beach, Fla., businessman, entrepreneur and high-tech investor is considering a purchase proposal with Canadian partners, people familiar with the situation told the newspaper.
Sculley told The Globe and Mail he couldn't comment, but said, "I've been a longtime BlackBerry fan and user."
BlackBerry had no immediate comment on the report.
"The only thing I would say is, I think there's a lot of future value in Blackberry," Sculley told the newspaper Wednesday.
"But without experienced people who have run this type of business, and without a strategic plan, it would be really challenging," he said.
"Whoever buys it would have to have a strategic plan that was credible and could succeed, and they would want to have an experienced team that would be able to implement that plan," said the executive who ran Apple from 1983 to 1993.
During Sculley's leadership of the company known at the time as Apple Computer Inc., sales increased to $8 billion from $800 million.
But his tenure, after a successful presidency of PepsiCo Inc., was controversial in part because of clashes he had with founder Steve Jobs over strategy.
Jobs, who had lured Sculley to Apple from PepsiCo., tried to oust Sculley in 1985 through a boardroom coup. But Apple's board sided with Sculley, who was chief executive officer, and removed Jobs from his managerial duties as head of the Macintosh division. Jobs then resigned.
Jobs returned to Apple in 1996, launching the iPod portable media player, new Mac computers and the iPhone. The iPhone not only revolutionized the smartphone industry but also led to BlackBerry's struggling surrender of its market leadership.
Sculley's reported interest in BlackBerry would be the latest in a series of potential bidders for the Waterloo, Ontario, company, which said in August it would examine its options, including a sale, joint ventures and strategic partnerships.
Chinese PC and smartphone giant Lenovo Group Ltd. is pursuing a possible deal, The Wall Street Journal reported last week.
Other companies considering acquiring BlackBerry include Cerberus Capital Management LP and BlackBerry co-founders Mike Lazaridis and Douglas Fregin.
In addition, technology giants, including Google Inc., Cisco Systems Inc. and German software company SAP AG, are reported eyeing BlackBerry or parts of the business or its assets, The Globe and Mail has said.
All the other potential buyers and BlackBerry have declined to comment.
BlackBerry already has a preliminary $4.7 billion buyout deal with Fairfax Financial Holdings Ltd., a Canadian insurance company that is one of BlackBerry's largest shareholders.
BlackBerry, ceding market share to rivals including Samsung Electronics Co. as well as Apple, reported a nearly $1 billion quarterly loss last month and said it would slash 40 percent of its workforce.