MD-11 Captain reported an engine malfunction at cruise related to low oil pressure. The Captain directed a precautionary shutdown of the engine and a diversion to an alternate airport and landed.

Narrative

Approximately 2 hours into flight; level at FL380; I scanned engine instruments and noticed the #3 engine Oil quantity ambered box 4 (qts). No other alerts or warnings presented. Additionally; other engine parameters were normal. We did not notice if the drop to 4 qts was instant or a gradual loss. Soon after; the amber boxed 4 changed to a simple white 4; and alternated back n forth. We referred to QRH; which directed us to monitor. We made contact with dispatch and maintenance control to discuss further. Since this was planned flight to ZZZ; we the crew; decided it was not a good idea to continue and would require to divert. We discussed ZZZ1; 200 nm away and ZZZ2; 400 nm or so. Quantity stayed steady at 4qts. Dispatch suggested ZZZ3 as preferred field. We said ok since engine was running and no further decrease in oil qty. We coordinated with ZZZ4 center and we're given clearance to ZZZ3. We planned to land with 3 engines operating. About 10 min later; quantity decreased to 3 qts. At this time we decided that an in flight shutdown would be required according to QRH to prevent engine seizure. We were at about 380;000 weight and did not want to shut down at FL380; so we requested a descent to FL300. During descent; oil dropped to 1qt. At FL300 FO and I ran engine shut down in flight checklist while FO flew jet. FL300 was correct altitude for engine-out cruise at our weight. Once shutdown; informed ZZZ4 center that we were [requesting priority handling]. ZZZ4 offered their assistance and we said we'd like to continue to ZZZ3; and remain at FL300; no assistance required at this time. ATC replied that ZZZ1 was about 65 miles and ZZZ2 about 200. We said ZZZ1 was too close (that would cause us to rush). ZZZ3 weather was basically clear and light winds. We would be starting descent in about 80 miles and ZZZ2 would be our backup plan. Aircraft had no problem maintaining FL300. ATC gave us direct routing to ZZZ3; and eventually altitudes and distance commensurate with descent profile and terrain. I briefed an ILS auto-land approach to RWY XX at ZZZ3. We were given direct to ZZZZZ and cleared approach. I took control of aircraft at FL200; eventually leading to uneventful landing at about XA:00. We cleared runway onto parallel taxiway where Fire/Rescue met us. We said no assistance required and they can check out #3 if they wished. One truck inspected and nothing appeared abnormal. We continued to park on #1&2 running; to tow-in gate XX. Outstanding support and teamwork by my crew.Side note: during initial cockpit preflight check; I noticed #3 engine oil quantity at 28 qts; while #1=23 & #2=21 qts. I briefed crew to watch for oil gulp during start up and we did get the gulp where oil quantity dropped to 23 qts. No abnormalities concerning this engine during taxi; takeoff or climb to cruise.