"We've made no decisions," Axelrod said on NBC's "Meet the Press."
President Barack Obama announced in November a plan to try Khalid Sheikh Mohammed, accused of plotting the 2001 attacks, and four alleged co-conspirators in federal court in New York about a quarter-mile from where the World Trade Center towers stood before being destroyed on Sept. 11.
New York City Mayor Michael Bloomberg said on Jan. 27 he wanted the trial moved, a change from November when he said he supported holding it in lower Manhattan. He said security for a trial in lower Manhattan could cost as much as $1 billion.
"Any community in America is going to object in the same way that New York finally did to these people being put on trial in the United States in civilian courts," said Senate Republican Leader Mitch McConnell, of Kentucky, on CNN's "State of the Union."
Axelrod said authorities had decided to hold the trial "near the site of the crime itself."
"Since then, the mayor and the police chief and others have changed their minds and said they thought it would be too logistically difficult and too expensive," Axelrod said. "We have to take that into consideration and we're doing that now."
Sen. Charles Schumer, a Democrat from New York, said he had lobbied the Obama administration to not hold the trial in New York City after speaking with Bloomberg and Police Commissioner Ray Kelly. Schumer stopped short of saying that the White House had decided to move the trial's location.
"I've encouraged the administration to find suitable alternatives and they appear to be doing just that," Schumer said at a New York news conference Saturday. "They have made no commitments yet, but to me it's pretty obvious that they cannot have these trials here in New York."
The Obama administration's approach to fighting terrorism, and its decisions to try the Sept. 11 suspects in civilian court, has been under assault by Republicans including Sen. Jeff Sessions (R-Ala.) ranking minority member of the Judiciary Committee.
The trial should be before a "military commission," Sen. Lamar Alexander (R-Tenn.) said on the "Fox News Sunday" program yesterday. "We have to make distinction between a kid who breaks into a sandwich shop in Detroit and a Nigerian terrorist who wants to blow up an airplane flying into Detroit."
"I think this is one of those things that sounded good in theory but in practice doesn't work," said Sen. Evan Bayh (D-Ind.) on Fox yesterday. "I don't think we should spend any more money than is absolutely necessary to try these guys."