B737-800 Captain reported an engine vibration indication that was out of limits.

Narrative

On arrival into ZZZ; I noticed the engine instruments on the lower DU (Display Unit) become displayed (normal procedure is to blank it after engine start so that if something goes out of limits; the display becomes active). Upon inspecting the parameters; I noticed that the engine vibration for engine #1 was displaying in reverse radio and displaying as high as 4.5. I directed the FO to open the QRH procedure for high engine vibration. We did not feel any abnormal vibration in the flight deck. We followed the checklist - per the checklist; I disconnected the autothrust and reduced the #1 engine thrust until the vibration indicated less than 4 units. The indication fluctuated from as high as 4.5 to as low as 2.0; even after reducing thrust. The indication occasionally blanked. Out of an abundance of caution; we [requested priority handling]; and I flew the ILS to runway XXR with the #1 engine at idle - doing so; the vibration indication did not return to 4.0 or above. Landing was normal; and ARFF (Airport Rescue and Firefighting) followed us to the gate. I made an AML (Aircraft Maintenance Logbook) entry upon arrival at the gate; detailing the indications we saw; and the fact that no abnormal vibration was felt.Cause: Upon discussion with each other and Maintenance; we assumed the indication was faulty; though we treated it as if high vibration was occurring for the duration of the event.