White House Press Secretary Jay Carney left the door open to the idea that President Obama would offer his sometime rival, Mitt Romney, a job in the administration to help make government more efficient.

“I really just don’t have a readout on that,” Carney replied when asked by reporters if Obama offered Romney a job during their lunch meeting today. “There was not an agenda that involves that kind of proposal  — that I’m aware of . . . I can’t dictate what the president says or what Governor Romney says but I don’t think that’s what this was about.”

Carney said that Obama wanted to get Romney’s insight on government efficiency given his experience as an effective manager, such as when he ran the Salt Lake City Olympics after leaving Bain Capital.

“Governor Romney clearly knows how to manage an operation,” Carney said, noting that Obama feels “passionately” about the need for an efficient government. “Somebody with Governor Romney’s experience clearly would have insight in how to maximize efficiency in something like the federal government.”