The chief executive has been recovering well and is expected to return to work on schedule later this month, though he may work part-time initially.
Jobs didn't respond to an e-mail requesting comment.
"Steve continues to look forward to returning at the end of June, and there's nothing further to say," said Apple spokeswoman Katie Cotton.
When he does return, Jobs may be encouraged by his physicians to initially "work part-time for a month or two," a person familiar with the thinking at Apple said. That may lead Tim Cook, Apple's chief operating officer, to take "a more encompassing role," this person said. The person added that Cook may be appointed to Apple's board in the not-too-distant future.
Apple has previously drawn criticism from some shareholders over what they have called limited disclosure of Jobs's health problems, which began in 2004. In this case, it is unclear whether the surgery is material because Jobs was already on leave. Material information like that must be disclosed only "if you are asking shareholders to make a decision based on [that] information," said John Olson, a senior partner at Gibson, Dunn & Crutcher in Washington. "You can't expect the company to give a blow-by-blow account of Steve Jobs's health."
But once Jobs resumes work, the company will have to be "very careful" about what it says "about his health and his prognosis," Olson said. The attorney, who counsels corporate boards on governance issues, has never advised Apple's board.
At least some Apple directors were aware of the CEO's surgery. As part of an agreement with Jobs in place before he went on leave, some board members have been briefed weekly on the CEO's condition by his physician.