Police do not have any footage of the flying machines at the airfield and are relying on accounts from witnesses and the discovery of a damaged device.
The revelation by Detective Chief Superintendent Jason Tingley came after the couple arrested by Sussex Police on Friday night were released without charge.
Asked about speculation there never was a drone, he said: “Of course, that’s a possibility. We are working with human beings saying they have seen something.
“Until we’ve got more clarity around what they’ve said, the detail – the time, place, direction of travel, all those types of things – and that’s a big task.”
Mr Tingley said one of the “working theories” was that the damaged drone found close to the airport in Sussex was responsible for causing the disruption.
“Always look at it with an open mind, but actually it’s very basic common sense that a damaged drone, which may have not been there at a particular point in time has now been seen by an occupier, a member of the public, and then they’ve told us, ‘we’ve found this’.
“Then we go and forensically recover it and do everything we can at that location to try and get a bit more information.”
The detective said the arrests made on Friday night were the result of a tip-off from a member of the public.
“I’m completely satisfied the arrests were lawful, bearing in mind the burden of proof and likely suspicion at the time of arrest,” he said.
“Obviously we had to be sure prior to release, in terms of that investigation, they were no longer suspects.”
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Mr Tingley added: “I won’t apologise, but what I will say is we really do appreciate their co-operation and we have put a lot of effort and resources into supporting them when they were released from questioning.”
Police are working through information relating to “persons of interest”, investigating more than 67 drone sightings and forensically examining the damaged drone.
Mr Tingley said he could not rule out the risk the culprits would strike again at Gatwick or another airport, but added he hoped someone would come forward with the vital clue.
He insisted the investigation was not “back to square one” and added: “We have a number of lines of enquiry and persons of interest. We are still progressing those lines of enquiry, including house-to-house enquiries around the sightings of the drone.”
Gatwick Airport has offered a £50,000 reward through Crimestoppers for information leading to the arrest and conviction of those responsible for the chaos.
Around 1,000 flights were cancelled or diverted after drones were spotted inside the perimeter of the UK’s second biggest airport on Wednesday and approximately 140,000 passengers were affected over a three day period.
Labour has called for an independent inquiry after accusing the government of failing to act on the risks posed by drones at Gatwick.
Shadow transport secretary Andy McDonald claimed there were missed opportunities to prevent the airport from coming under such an attack.
“The government was repeatedly warned about the risks posed by drones to aviation but failed to act,” he said.
Additional reporting by Press Association