Kennedy has been asked to take on the role and is being vetted, a Democratic source told CNN Monday.
Kennedy, who flirted with a Senate run in New York after Hillary Clinton became Secretary of State, backed both Obama runs and co-chaired his vice presidential search committee in 2008.
After she withdrew from Senate consideration for "personal reasons," Kennedy's name was floated by the political media for several possible diplomatic posts, including the United Kingdom and the Vatican.
Tokyo is considered a policy-heavy post, as Japan is the U.S.'s largest economic partner and a military ally, and American troops maintain a presence on Japan's Okinawa island.
Kennedy has degrees from Harvard and Columbia Universities, and held a variety of positions at non-profits including the JFK Library and the American Ballet Theatre.
Current Ambassador John Roos has been in Tokyo since 2009.