The Wall Street Journal reports that Jobs received a new liver in Tennessee about two months ago, however, this has not been confirmed by Apple.
There has long been speculation over Jobs' health, who has been successfully treated for cancer of the pancreas as far back as 2004.
An appearance at an Apple conference in 2006 prompted many to comment on his gaunt appearance and apparent loss of energy, although at the time the company said he was healthy.
Since the beginning of 2009, Jobs has been signed off work. In January he wrote a letter to the Apple community explaining that doctors had discovered a hormone imbalance which had caused him to lose weight.
Jobs expected to recover by the spring, however a week later he said he would be taking leave as the problem was more serious than intially thought.
At the same time he promised that if he were unable to fulfil his duties as Apple CEO he would be "the first one to step up and tell our board of directors".
A spokeswoman for Apple told the Wall Street Journal: "Steve continues to look forward to returning at the end of June, and there's nothing further to say."
In 2008, Bloomberg briefly published an obituary of the businessman by mistake.