Two of the unmanned flying craft were reported to have been seen near to the terminal on Monday morning (October 10).
Flight crew at Heathrow altered authorities after spotting one of the devices close to the airport’s transport hub, while another sighting was reported near to the Queen Mother Reservoir.
The Metropolitan Police aviation team said on Twitter: "Officers are responding to two reports of a drone sighting near the approach to Heathrow. This is both dangerous and illegal."
A Scotland Yard spokesperson said: "At this stage it is not believed that any aircraft were at risk. However, members of the public are advised to read guidance issued by the Civil Aviation Authority before flying a drone."
A Heathrow spokesperson said: "Heathrow’s top priority is the safety of our passengers and colleagues.
"Anyone operating an unmanned aerial vehicle has an obligation to know the rules and ensure they are capable of operating it safely.
"Doing so in proximity to an airfield or aircraft is both illegal and clearly irresponsible.
"Stronger regulation and enforcement action must be a priority for the Government to ensure that the airspace around British airports remains among the safest in the world.
"We will continue to work with our industry partners to ensure that any violation of airspace is fully prosecuted."
The investigation into the drone sightings follows increasing concerns from authorities over the use of the devices near airports.
Last month, general secretary of the British Airline Pilots’ Association (Balpa) Brian Strutton said it was “only a matter of time” before a “major accident” was caused by a drone collision.