The newspaper reported that the discussions were not explicitly aimed at recruiting a new chief executive, but more an exploration of options.
Those directors did not appear to have been acting on behalf of the entire board, and it was unclear if Jobs, who has been on leave for undisclosed medical reasons, was aware of the discussions, according to the report. It said Jobs told the newspaper in an email: "I think it's hogwash."
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Jobs is a survivor of a rare form of pancreatic cancer who underwent a liver transplant in 2009. His health has been in the spotlight for years.
Chief Operating Officer Tim Cook and the rest of Apple's upper echelons have won Wall Street's confidence by leading the company capably in his absence.
Shares in Apple, which is due top report quarterly results later on Tuesday, were up 0.6 percent at $376.15 in late afternoon.