The technology giant's shares were worth $633.38 last week as its stock price rose above Google's for the first time, the Daily Mail reported Friday.
Brian White, of Topeka Capital Markets, then claimed Apple's sky-high share price will hit four figures within 12 months - making the company worth $1 trillion.
Apple store at San Francisco. Photo: AFP
He said in his report: "Apple fever is spreading like a wildfire around the world."
Gene Munster, of Piper Jaffray, followed that up by claiming Apple stock will hit $1,000 - but by 2014.
The company, based in Cupertino, California, is already the most valuable company in the world currently valued at $590.82 billion, according to the newspaper.
Just a year ago the shares were changing hands at $341. In January, Apple revealed it had more than doubled its profits to $13.06 billion, compared with $6 billion for the same quarter in 2010.
Tim Cook, Apple's chief executive who took over from the late co-founder Steve Jobs, said: "We could have sold more if we'd had more supply. We could not be happier."
Apple's growth is expected to be driven by sales in China, where January's launch of the iPhone 4S triggered a near riot in Beijing, the Mail said.
Earlier this year Morgan Stanley analyst Katy Huberty predicted Apple could sell 40 million iPhones in China this year. Apple is also expected to move into the TV market after the launch of its set-top box Apple TV.