The plane was escorted in to land by the Royal Air Force (RAF) following information received by the pilot.
Greater Manchester Police said officers were treating it as a "full emergency" as they did not know "how genuine this threat is".
Chief Superintendent John O'Hare said the safety of those on board was "paramount".
It is understood the plane involved is an Airbus A330, which was escorted by a Typhoon from RAF Coningsby in Lincolnshire, the BBC reported.
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"We don't know how genuine this threat is but it is absolutely vital we deal with the situation as a full emergency.
"As a result people will see the police and other agencies at the airport and on the airfield. At this time I would urge them not to be alarmed.
"Our response will be as comprehensive as it is proportionate, with the safety of those on board and in and around the airport our paramount concern," O'Hare said.