A very faint constant sound can be normal on this lens. Based on the reports here, Panasonic service considered it normal, and another new copy made the same noise. One likely cause is that internal stabilization or other electronic/mechanical systems remain energized even when OIS is switched off, so the lens may not be completely silent at idle.

Another possibility on some camera/lens combinations is small aperture adjustments during metering, which can create a chattering sound. You can check that by looking into the front of the lens to see whether the aperture is moving in sync with the noise.

If the lens focuses and zooms correctly, the sound is extremely quiet, and it behaves the same on multiple bodies, that points more toward normal operation than a defect. If the noise becomes loud, affects images, or is accompanied by focusing/stabilization problems, then it would be worth having it inspected again.