John McCain is the expected Republican presidential nominee. Obama is closing in on the Democratic nod.
Asked about the suggestion and how seriously it was being considered, David Axelrod, Obama's chief campaign strategist said: "Very seriously."
"We believe that is the most significant election we've faced in a long time," he said on "Fox News Sunday."
"We're at war. Our economy is in turmoil. And we've got so many challenges that the people of this country deserve a serious discourse, and it shouldn't be limited necessarily to three kind of very regimented debates in the fall," he added, referring to those sanctioned by a presidential commission.
Axelrod declined to discuss details. So did aides to McCain, saying they would rather wait until they have an official opponent.
"We ought to begin sooner, and we ought to have a free-flowing conversation about where we want to take this country," Axelrod said. "So you know, we're interested in that proposal and eager to sit down and talk about it."