Hillary Clinton, who generates speculation about a potential 2016 presidential run wherever she goes, had tongues wagging anew on Monday by sitting down for lunch with President Barack Obama at the White House.

But not just at the White House. The one-on-one session was on the private patio just steps away from the Oval Office, which is, as everybody knows, where any future President Clinton would work.

Clinton served as Obama’s secretary of state during his first four years as president, stepping aside in February. She accepted that job after losing a tight and sometimes acrimonious battle to Obama for the 2008 Democratic presidential nomination.

White House spokesman Josh Earnest came under close questioning about the lunch in the daily news briefing.

“Somehow I knew somebody was going to ask about that today,” he chuckled.

It was “largely friendship” that was on the agenda for the tete-a-tete, he said.

“So it’s not a working lunch, as much as it is an opportunity for the two who saw each other on a pretty frequent basis over the course of the last four years to get a chance to catch up,” Earnest added.

On the menu were grilled chicken, pasta jambalaya and salad. An official White House photograph showed Obama, the 44th U.S. president, and Clinton, who has not yet made clear whether she will try to become the 45th, smiling with plates of salad before them.

This was enough to generate a welter of headlines like this one from MSNBC: “44 meets 45? – Obama and Clinton do lunch.”

Clinton has been giving speeches and writing a book – and keeping the political analysts guessing about whether she will attempt a second run for president.

Clinton insiders say she has not made up her mind, but much of political Washington has already decided that she is, in fact, running. A “Ready for Hillary” political action committee has already formed in support of her, and many high-profile Democrats have signed on to help out.

Caught somewhere in the middle is Obama, who has to show support for both Clinton and his loyal vice president, Joe Biden, who is pondering his own 2016 run.

“I can die a happy man never having been president of the United States of America,” Biden told GQ magazine. “But it doesn’t mean I won’t run.”

Another tantalizing detail emerged later in the day: Clinton will be having breakfast with Biden at the vice president’s residence on Tuesday.

Clinton, the wife of former President Bill Clinton, is the overwhelming favorite among Democrats to be their party’s nominee, far outpacing Biden, according to a variety of polls. DM

Photo: President Barack Obama has lunch with former Secretary of State Hillary Rodham Clinton on the patio outside the Oval Office, July 29, 2013. (Official White House Photo by Chuck Kennedy)