I notice there is a similar problem reported in flashlights but not quite the same.
I have renovated my house using LED's for most of the lighting and of the 50 or so fittings 2 glow faintly all the time they are switched off.
When the lighting circuit on the fuse board is switched off they do go out. This suggests a faulty switch but they are on different switched circuits and the other LED's on the same circuit do not glow.
Could it be inductance from a nearby lighting circuit or is there some other explanation?