Captain reported a nose tire and wheel assembly departed the aircraft nose gear axle during taxi. The flight crew was still in the ramp area and parked for maintenance action.

Narrative

We picked up this jet initially at ZZZ1 for the turn to ZZZ and back. The left-seater was an upgrading Captain (Supervisor) and the right seater was an OE Captain (me). Before the Student-Captain's walk-around; the Mechanic told us the left nose wheel tire is OK to go; but would've been changed if he had more time. There was a spot on the tire where threads could be seen. We flew uneventfully to ZZZ and went inside the ZZZ Gateway awaiting our return leg to ZZZ1. Coming out to the jet for preflight; the ZZZ Mechanic was in the process of replacing the worn tire. During the taxi out to Runway XXL; the Student-Captain taxied cautiously and slowly. Our initial taxi instructions were to hold short of Taxiway 1 (on Taxiway 2 for a Company jet taxiing north on Taxiway 3. While holding; we accomplished pre-takeoff flows; briefing; and checklist. After the Company jet passed us; we taxied north on Taxiway 4 which is where I noticed a slightly unusual vibration and noise that seemed to come from the nose gear. We discussed the jet's handling characteristics and the Captain-Student said there weren't any pulling or dragging indications; but we decided it would be best to get a quick look-over by a Mechanic. We were still close to the ramp and coordinated with ATC and ZZZ Ops for the return to the Ramp. After completing a wide turn to the south on the de-ice pad; the vibration and noise seemed to go away; but we still thought it would be best to get eyes on the exterior of the jet to be certain. Since it was dark; we had no visual clue the wheel rolled off the jet an into the grassy area between the de-ice pad and Runway XXL. After pulling back onto the Ramp; the Mechanic hooked up to the intercom. We asked him if he saw any damage to the nose gear area to which he said that we were missing a tire. We immediately notified ATC that we lost a wheel; but not certain of its exact location. We provided our Taxi route to them for a search. We performed shutdown and secure procedures and checklists. I don't have any recommendations for preventing a future occurrence.