Urgent question! Can I get an Italian ID card? (Milan)

Hi!

I am trying to renew my German passport while in Milan (it expires in a month's time and I will be here for several months).

The German consulate is demanding I present them with an Italian ID card. As far as I know, I am not eligible for one, having not been born in Italy. Am I wrong? If I can apply for one, where would I go?

Any help would be hugely appreciated!
Best regards,
Katharine