Apple Inc CEO Steve Jobs displays a redesigned iPod Nano at Apple's "Let's Rock" media event in San Francisco, California, September 9, 2008. REUTERS/Robert Galbraith

SAN FRANCISCO (Reuters) - Shares of Apple Inc fell as much as 2 percent on Tuesday after technology website Gizmodo reported a “rumor” that Chief Executive Steve Jobs’s health was declining.

A spokesman for Apple declined to comment on the rumor.

When asked about Jobs’s health, the spokesman said “if ever Steve or the board of directors decided that he was no longer capable of doing his job as CEO of Apple, I’m sure they will let you know.”

Gizmodo quoted a “solid source,” which it did not identify, as saying that Jobs’s “rapidly declining” health was the real reason behind his decision to cancel a keynote speech at next week’s MacWorld conference. It titled the report “rumor.”

Apple shares had been trading up 1.5 percent at $87.92 before moving sharply lower. The stock then recovered to trade down about half a percent at $86.15 by mid-afternoon.

“The main reason why Apple shares have sold off midday is that a website reported that Steve Jobs health is getting worse, citing an unidentified source,” said William Lefkowitz, an options strategist at brokerage firm vFinance Investments.

“However, this is not the first time Steve Jobs health has come into question. In the past, this has created large fluctuations in Apple stock,” he said.

(Reporting by Doris Frankel in Chicago and Gabriel Madway in San Francisco; Editing by Bernard Orr)