Talking to Larry King Live, the 73-year-old admitted that he is upset by the repeated jokes which have now happened four times, the latest of which began after users on Twitter began typing "Bill Cosby Died" into their posts on the website.
"I don't want this person, or whatever, I don't want them to do this anymore," he said.
"I found out when my daughter called the house. [She said}, 'Dad, people are calling me, are you alright?' Maybe psychiatrists will say I'm feeding this person's ego, but I just want to say to friends of that person, just tell them to stop. Because it isn't funny."
Cosby also responded to the rumours via his own Twitter page.
"Emotional friends have called about this misinformation. To the people behind the foolishness, I'm not sure you see how upsetting this is," he wrote.