Pilots spotted a gadget with multiple arms and up to eight rotors pass by the right hand side of the plane as it was preparing to land.
Both pilots exclaimed: "Was that a drone? At 10,000 feet!", air safety experts UK Airprox Board (UKAB) said.
The drone was estimated to be about 98ft (30m) away from the plane and "safety was not assured", UKAB added.
Large drones are not permitted to fly above 400ft (121m) or within proximity of airports or airfields.
It happened on 11 November 2016, so quickly the Airbus A320 pilots said they had "no time to react".
The risk posed was classified as 'b', the second most serious out of five in which the safety of the aircraft may have been compromised.
Police officers were alerted at the time but they did not find the operator.
It was one of four near misses between aircraft and drones in the latest UKAB monthly report, and brings the total in the past 12 months to 59.
Ministers are considering mandatory registration for new drones to help regulate their use and the Department of Transport is consulting on how to improve drone safety.
A passenger plane had a near-miss with a drone at 10,000ft as it approached Heathrow Airport.