If successful, by the end of the term beginning 2007, he would be 81, and would have spent nearly two-thirds of his life on Capitol Hill.
Kennedy, 67, experienced a succession of traumas since last winning reelection in 1994, including the deaths of his mother in 1995 and of two nephews, Michael Kennedy and John F. Kennedy Jr. in the past 21 months.
The senator said he has "every expectation" that he will run in the next two elections for his Senate seat.
"I can't see him enjoying a life of leisure," his son, Rhode Island Rep. Patrick J. Kennedy, told The Boston Globe. "For him, the most exciting thing is being in the midst of a legislative battle. He's at home in the Senate."
Sen. Strom Thurmond, R-S.C., is the longest-serving senator in the history of the United States. If the 96-year-old retires at the end of his term in 2002, as planned, Thurmond will have been a senator for 47 years.
Kennedy, currently the ninth-longest serving senator of all time, was elected in 1962.