The potential candidate, 49, the middle child of the late U.S. Sen. Edward M. Kennedy and his former wife, Joan, runs a law firm in New York City and is an activist for the disabled.
Kennedy lost a leg to cancer when he was 12.
"No one knew Lieberman would be getting out. I think Teddy would be the odds-on favorite were he to enter the race. But I don't know if this is the right time for him," a Kennedy friend told Thursday's Boston Herald.
Kennedy's inspiring eulogy at his father's funeral in 2009 prompted observers to focus on him for public office, the Herald said.
Susan Bysiewicz, a former Democratic Connecticut secretary of state, said this week she would run and a recent poll indicated she would beat Kennedy in a primary.
Other potential candidates include Democratic U.S. Reps. Chris Murphy and Joe Courtney, both D-Conn., and Republican Linda McMahon, who lost a 2010 Senate election.
Notable deaths of 2014 [PHOTOS]