The incident occurred Tuesday afternoon, The Washington Post reported.
The immediate cause appeared to be a shift in wind patterns that led to a change in aircraft approach routes that was not completely communicated to air traffic controllers.
All three jets were operated by US Airways. They were carrying a total of 193 people.
Disaster was averted when a controller realized she had made a mistake and called the pilot of the incoming plane, telling him to abort the landing and circle the airport. No one was hurt.
An official said the problem with the change in traffic patterns was compounded by simple sloppiness, the newspaper reported.