Sources familiar with the situation said Obama signed off on Kennedy's nomination but her vetting has yet to be completed, Bloomberg first reported Wednesday.
Kennedy, 55, would replace Ambassador John Roos.
Kennedy is one of several Obama political supporters and donors being reviewed for ambassadorships to top U.S. allies, Bloomberg said.
Obama also is considering John Emerson, president of Capital Guardian Trust Co., as U.S. ambassador to Germany, and Marc Lasry, chief executive officer for Avenue Capital Group LLC, as the U.S. envoy to France, the sources said. Obama also reportedly was favoring Matthew Barzun, finance chairman of Obama's presidential campaign, for the ambassadorship to Britain.
White House press secretary Jay Carney declined to comment, as did Lasry. Bloomberg said Kennedy and Emerson did not respond to a request for comment.