It comes after a couple were released without charge after two nights in custody.
The Mirror reports Sussex Police insisted it was "not back to square one" and was examining a damaged drone found near the airport. The force said it was actively investigating 67 sightings.
However, BBC News reports detective chief superintendent Jason Tingley said previously no footage of a drone had been obtained and there was "always a possibility" the reported sightings were mistaken.
About 1,000 aircraft were cancelled or diverted, affecting 140,000 passengers, during three days of disruption at the airport last week.
Gatwick airport has offered a £50,000 reward, through Crimestoppers for information leading to an arrest and conviction, and another £10,000 has been put up by the charity’s chairman Lord Ashcroft.
Tingley added he hoped the money would persuade someone to come forward with a vital lead. He said there were some "persons of interest" but warned he could not rule out the risk the culprits would strike again at Gatwick or another airport.
The Mirror reports a government source said that the disruption at the airport would be discussed in a conference call on Christmas Eve, which ministers would be involved with.
Gatwick said in its latest statement: “We respect the decision from the police [to release the couple without charge] this morning and will continue to work with them on their investigation.
“We can confirm that Gatwick is offering a £50,000 reward through Crimestoppers for information leading to the arrest and conviction of those responsible for the criminal act that disrupted our flights over three days at the airport.”
If anyone has information, they should contact Crimestoppers anonymously on 0800 555 111 or report information through their anonymous online form at Crimestoppers website.
Payout on the reward will be made only if the information is given to Crimestoppers first.