WASHINGTON — When is a lunch more than just a midday meal? When the two diners are President  Obama and Hillary Rodham Clinton, and inquiring minds want to know who, if anyone, the president will endorse in 2016.

A summertime meal shared by Obama and his rival-turned-ally threw the political speculation machine into overdrive Monday, highlighting how closely both are being watched for signs of their intentions in the next presidential race.

For Clinton, it’s a question of whether the former first lady will take the plunge, launching another campaign eight years after she lost to Obama in a hard-fought primary. For Obama, it’s about dueling loyalties to two of his closest advisers who would both covet his endorsement: Clinton and Vice President Joe Biden, who is also said to be eyeing the Oval Office.

Such questions set the table for a midday powwow over salad, grilled chicken and pasta jambalaya whipped up by the White House chef and served al fresco on the patio just outside the Oval Office.

Will Clinton tip her hand? Will Obama offer his support? Or will the two dive deep into current events — bloodshed in Egypt, for instance, or a budding new round of Mideast peace talks that eluded Clinton as secretary of state?

In all likelihood, none of the above.

“The purpose of the lunch was chiefly social,” said White House spokesman Josh Earnest, calling it a “chance to catch up” and adding that Obama had initiated the invitation. “Secretary Clinton and the president have developed not just a strong working relationship, but also a genuine friendship.”

So what are the chances that Biden popped in for coffee and dessert, a casual reminder that he’s still the one with the office closest to Obama’s?

“I think the table was set for two,” Earnest said.

Not to worry — Biden will have his own chance to shoot the breeze with his former Senate colleague and 2008 primary opponent on Tuesday. The White House said Biden and Clinton will have breakfast together at the Naval Observatory, the vice president’s official residence.

While in the West Wing Monday, Clinton stopped by the office of Susan Rice, Obama’s national security adviser who served as U.N. ambassador under Clinton, and visited with John Kerry, Clinton’s replacement as secretary of state.