Kelly’s name has been floated as a top contender to take over for DHS Secretary Janet Napolitano, who is leaving to head the University of California school system.

President Obama sang Kelly’s praises in an interview last month, saying that he would “want to know” if he was interested in seeking the post.

“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 told Univision.

The president called New York’s top cop “one of the best there is” and an “outstanding leader.”

But Kelly only referred back to Obama’s remarks when asked on Sunday whether he had any conversations with the White House about possibly taking on the post.

Kelly has also attracted praise on Capitol Hill, with New York Sen. Charles SchumerCharles (Chuck) Ellis SchumerOvernight Health Care: Schumer calls for tying ObamaCare fix to children's health insurance | Puerto Rico's water woes worsen | Dems plead for nursing home residents' right to sue Crying on TV doesn't qualify Kimmel to set nation's gun agenda Trump knocks ‘fake’ news coverage of his trip to Puerto Rico MORE (D) telling reporters that he had recommended him for the position. 

A point of controversy for Kelly has been New York City’s “stop and frisk” policy, which has been implemented to new levels under his tenure as head of the largest urban police department.

Kelly defended the policy on Sunday, saying that violence would increase as a result of a federal judge’s recent ruling stating that the strategy is unconstitutional.