Critics have said the government's plan to try Khalid Sheikh Mohammed, the self-professed mastermind, and four alleged co-conspirators would require a large security cordon, hurt area businesses and afford the defendants certain legal rights in criminal court.
The proposed trial location is just blocks from where the World Trade Centre once stood before the September 11, 2001, attackers flew hijacked airliners into the Twin Towers.
Nearly 3,000 people were killed there, at the Pentagon and in a field in Pennsylvania during the co-ordinated attacks.
The trial is a major component of the broader plan of Barack Obama, the US president, to close the military prison at Guantanamo Bay, Cuba, and end what he sees as widespread legal abuses under his predecessor, George Bush.
Eric Holder, the US attorney-general, was considering other venues for the trials, according to one Obama administration official.
"We're considering our options," Dean Boyd, a justice department spokesman, said.
Several alternative sites have been aired, including towns outside New York city, a federal prison in Otisville and Stewart Air National Guard Base.
However each has its own logistical problems, meaning that a quick solution is unlikely.
The New York Times and Washington Post reported that the lower Manhattan courthouse was out of the running, citing unnamed administration officials.
However, one Obama administration official told the Reuters news agency that "no decision has been made."
Holder decided in November that the trials would be held in New York city, whose federal courthouse is connected to a fortified detention centre with a tunnel.
"Conversations have occurred with the administration to discuss contingency options should the possibility of a trial in lower Manhattan be foreclosed upon by congress or locally," another Obama administration official said.
Ray Kelly, the New York city police commissioner, said he believed the trials are "unlikely" to occur in the city.
The decision to reconsider the location comes as Obama faces increased political pressure to refocus his agenda.
Obama has been trying to push through a healthcare-overhaul initiative and to reduce the high US unemployment rate.