PA-28 pilot reported low oil pressure during cruise resulted in diversion to landing.

Narrative

Night VFR flight with a CFI from ZZZ1 to ZZZ2; though I was acting as PIC. Low oil pressure approximately 70 miles west of ZZZ. Oil annunciator light was flickering; and then I noticed the oil pressure gauge was reading in the yellow arc lower than normal. Tried to troubleshoot the problem by reference to the POH; and alerted ATC of the problem. The oil annunciator light then went from flickering to a steady glow; which I then advised ZZZ center on XXX.XX. A corrective action was taken to divert to ZZZ3; and overfly the Interstate in the event that I suffered an engine failure I would have a set place to land. ZZZ center informed me that ZZZ3's runway was closed per NOTAM and ZZZ4 was the next closest option. I then requested priority handling with Albuquerque center. I was handed off to ZZZ1 approach where I was given a bravo [airspace] clearance after I requested to overfly ZZZ4 at 9500 feet and circle down in the event the engine failed. I had a normal; uneventful landing. Oil pressure was at zero by the time I landed.