A319 Captain reported loss of engine oil during cruise. Crew shut down engine and diverted.

Narrative

In cruise in oceanic airspace; we were proceeding northeast on an airway approximately halfway between ZZZZZ and ZZZZZ1 waypoints. First Officer Person A noticed number 1 engine oil quantity down to 5 quarts.We began monitoring the oil level and 9 minutes later it dropped to 4.5 qts. We decided; if it continued to 4 qts; we would divert. 7 minutes later; It dropped to 4 qts and I advised ZZZ radio to relay to ZZZ [ARTCC] our intention to divert to ZZZ1. I deemed ZZZ1 as the nearest suitable airport in point of time. ZZZ1 has mainline maintenance and would be no issue with foreign customs for my crew and passengers in the event that the aircraft went out of service.We were already on our way and ZZZ [ARTCC] came back with clearance present position direct to ZZZ1. I informed dispatch of our intentions via ACARS.The oil level in number 1 dropped again to 3.5 qts and we brought number 1 thrust lever to idle. Informed the cabin crew of the divert and to expect a precautionary landing. Time to ZZZ1 was :40 minutes at that time. I then made a PA announcement to the passengers to inform them. FO initiated a drift down procedure at Mach .76. We asked for and were cleared to descend pilots discretion to FL240.With the thrust to idle; oil level seemed to stabilize at 5 qts and I decided to wait and see if it stayed there. Soon; however; oil level on number 1 dropped again and we shut it down to prevent damage. We were single engine for the remaining 30 minutes.We were vectored straight to ZZZ1. First Officer Person A was the pilot flying. and asked for runway XX. He made the visual approach and single engine landing.ZZZ1 priority handling equipment met us on the taxiway and followed us to gate XX.ZZZ1 maintenance inspection revealed an oil leak on number one engine.Cause: Causal factors were equipment related. The engine had an apparent oil leak.