King, a confidant of Kelly, told the New York Daily News on Wednesday that the top cop is "not saying no" to the idea.

Since Homeland Security Secretary Janet Napolitano announced that she planned to step down from her post to run the University of California system, Kelly's name has been mentioned as a possibility to replace her.

On Tuesday, in anĀ interview with Univision's New York City affiliate, President Obama said he would "want to know" if Kelly would be interested in taking the job.

"Mr. Kelly might be very happy where he is, but if he's not, I'd want to know about it because obviously, he'd be very well-qualified for the job," Obama said.