The New York Daily News, quoting an unnamed Kennedy associate, said that the Massachusetts Democrat would back his wife, Victoria Kennedy, if he is forced to resign. Kennedy, 76, was diagnosed earlier this week with a cancerous brain tumor.
"Discussions like that are not happening, and it's disgusting that people are even speculating," Kennedy spokeswoman Stephanie Cutter told the Boston Herald.
Howard Penn, longtime Kennedy friend and co-owner of Puritan Clothing, expects the senator to stay on the job.
"If he can keep doing his work, he will do it," Penn said. "It's hard to believe that he will be thinking about giving up his seat."
Under Massachusetts law, if Kennedy leaves before the end of his term, the seat would be filled by a special election. The seat was held by John F. Kennedy from 1952 to 1960, by a Kennedy friend from 1960 to 1962 and by Edward Kennedy ever since.