Earlier, Lincolnshire Police said the aircraft came down in a field off Langrick Road, which runs alongside the perimeter of the RAF station.
Road closures are in place around Dogdyke Road and Sandy Bank, with motorists asked to avoid the area.
RAF Coningsby is the home of the RAF’s Battle of Britain Memorial Flight (BBMF).
According to its website, BBMF operates six Spitfires, two Hurricanes, a Lancaster, a C47 Dakota, and two Chipmunk aircraft used for training. The aircraft are flown by regular RAF aircrew.