My Passat vibrates

That's the EVAP system purge valve. It's normal for that part to click while it's working.

The EVAP system captures and stores gasoline vapors so they don't get into our atmosphere. When the engine is running, the system dumps the stored hydrocarbons into the intake to burn them up. This valve is how the ECM controls the rate of dumping. The ECM will pulse the valve open/closed and watch for changes in the exhaust chemistry (O2 sensor). The pulses can be made longer or shorter to change the amount of flow.

Is your Check Engine Light on? Get the car scanned for trouble codes. The codes may offer some clues as to what is causing the rough idle.

You didn't say, or I missed it, does it vibrate when driven or idling (standing still)?

If at idle, possible bad motor mount(s).

Thank you.

I checked the mounts they're OK. I think it also produces noise, more than before ,when driven.

make sure you don't have a vacuum hose leak. check the L hose next to the coolant and inspect others too.