By Daniel Strauss - 01/28/13 01:31 PM EST
McLarty noted that Obama appointed Vice President Biden to lead a task force on producing recommendations on gun violence.
"I mean, he's put Vice President Biden on point in terms of some of these negotiations, and there may very well be some other very well-qualified candidates on the Democratic side, certainly on the Republican side," McLarty said. "It really is a little too far to speculate, but I think the president really, probably, most likely stays neutral.
"He's got a full plate ahead of him right now, he's probably concentrating on that," he added.
On Sunday, CBS aired a joint interview with Obama and Secretary of State Hillary Clinton, reigniting speculation about the 2016 presidential field. Clinton and Biden have both been mentioned as possible contenders for the Democratic nomination for president in 2016.
In the "60 Minutes" interview, Clinton and Obama both played down the possibility of the secretary of State running for president again in 2016. She previously said that she planned to retire from public life after finishing her tenure in Obama's Cabinet.
"I don't think, you know, either he or I can make predictions about what's going to happen tomorrow or the next year," Clinton said.