President Obama has only just started his second term but already, with the announcement that he and Hillary Rodham Clinton will appear on the CBS News program “60 Minutes” on Sunday for their first joint interview, he has set off speculation about whether his onetime rival is privately his choice for a successor.

Just five years after their epic battle for the Democratic presidential nomination, the two were to be interviewed by Steve Kroft of “60 Minutes” on Friday, just ahead of Mrs. Clinton’s last week as Mr. Obama’s secretary of state. …

“We wanted to do a joint interview as a way of thanks on her way out, and this seemed like a good format to do it,” said Mr. Plouffe, who suggested that Sunday’s show should be “quite the event.”