A330 Captain reported a message on ECAM stating Loss Hydraulic Quantity on the Green System after extending the landing gear for landing. The flight crew executed a go-around and ran the QRH and checklists and elected to divert to a nearby airport with a longer runway.

Narrative

On our final approach; after extending the landing gears in the down position and completing our landing checklist; we had a message on ECAM stating 'Loss Hydraulic Quantity on the Green System'. Executed a go-around and asked vector from ATC. Executed and followed the ECAM procedure. Requested priority handling and requested a diversion to ZZZ1. We were able to land safely.After our ECAM warning on our final approach; we executing a go-around so we could complete our ECAM procedure. Since we lost our green system we were unable to retract our main landing gear. The ZZZ airport is a very short landing runway and requires medium auto braking system but we lost our Normal/Auto Braking System; Nose Wheel Steering; and partial Flight Controls. We are trained to go and hold when a problem arises and complete our checklist; however; I had to make a quick decision to divert because we couldn't retract our landing gear and was burning a lot of fuel due to the drag. The FMS fuel calculation was inaccurate due to the gear extended in the down position. When we landed; we had approximately 7;200 lbs. of fuel remaining. If I requested a holding and we took our time to do our checklist; we would have lost a lot more fuel and could have run into more problems.I suggest that more fuel be allowed for all flights in the event of an emergency in the future.