The Airbus A320 was making its final approach to Glasgow Airport on 2 December when an object passed about 300ft underneath it.
The pilot of the aircraft said the risk of collision with the object, which did not show up on radar, had been "high".
A report by the UK Airprox Board said investigators were unable to establish what the object had been.
The A320 was flying with its landing lights on, in clear conditions and at an altitude of about 4,000ft above the Baillieston area of Glasgow, when the pilot and non-flying pilot saw an object "loom ahead" at a range of about 100m.
The object passed directly beneath the aircraft before either of the crew members had time to take avoiding action or had "really registered it".
But they both agreed that it appeared to have been blue and yellow or silver in colour with a small frontal area, but "bigger than a balloon".
The pilot asked the controller at Glasgow Airport if he was "talking to anything in the area" as he had "got quite close" to a blue and yellow aircraft, travelling in the opposite direction, which had passed just below him.
The controller stated that he was not talking to anyone else in that area and that nothing was seen on radar.
Search action was taken with no result and the A320 pilot stated his intention to file a report to Airprox, which investigates near misses.
Air traffic control said they had no trace of any other objects in the area at the time of the incident, although the radar at Prestwick did spot an "unidentified track history" 1.3 nautical miles east of the A320's position 28 seconds earlier.
Once the aircraft had landed, the pilot told the Glasgow Aerodrome Controller: "We seemed to only miss it by a couple of hundred feet, it went directly beneath us. Wherever we were when we called it in it was within about 10 seconds. Couldn't tell what direction it was going but it went right underneath us."
When asked if he thought it may have been a "glider or something like that" the pilot replied: "Well maybe a microlight. It just looked too big for a balloon."
The Airprox report concluded: "Investigation of the available surveillance sources was unable to trace any activity matching that described by the A320 pilot. Additionally there was no other information to indicate the presence or otherwise of activity in the area."
The report said the Airprox board had been of the opinion that the object was unlikely to have been a fixed wing aircraft, helicopter or hot air balloon, given that it had not shown up on radar.
It was also thought that a meteorological balloon would be radar significant and unlikely to be released in the area.
A glider could not be discounted, the report said, but it was unlikely that one would be operating in the area because of the constrained airspace and the lack of thermal activity because of the low temperature.
Similarly, the board believed that a hang-glider or para-motor would be radar significant and that conditions precluded them, as they did para-gliders or parascenders.
The report stated: "Members were unable to reach a conclusion as to a likely candidate for the conflicting aircraft and it was therefore felt that the board had insufficient information to determine a Cause or Risk".
The Airprox report included a transcript of the conversation that took place between the aircraft and the controller at 12:55:
A320: "Glasgow Approach [A320 C/S]"
EGPF: "[A320 C/S] pass your message"
A320: "Er yeah we just had something pass underneath us quite close [1255:30] and nothing on TCAS have you got anything on in our area"
EGPF: "Er negative er we've got nothing on er radar and we're n- not talking to any traffic either"
A320: "Er not quite sure what it was but it definitely er quite large [1255:40] and it's blue and yellow"
EGPF: "OK that's understood er do you have a an estimate for the height"
A320: "Maybe er [1255:50] yeah we were probably about erm four hundred to five hundred feet above it so it's probably about three and a half thousand feet."