Rattle at some point of clutch engagment when the pedal is coming up

I can hear rattling noise when I am releasing the clutch pedal. The problem is as follows. I push the clutch pedal to the end, change to the first gear, and start releasing the pedal (without pushing on the acceleration pedal for this test). At some point before the full engagement I can hear strong rattling noise from my car until the clutch pedal is fully up (at this point there is a little to no rattling noise). The point is that even if I push on the acceleration pedal, and at the same time release the clutch pedal faster to the full engagement point, I can still encounter this rattling effect (although not as strong as before) somewhere before the clutch pedal is fully up. This also happens for shifting to the second gear, but not for upper gears nor for the reverse gear. Is this normal?

2011 BMW 116d