Traveling to Italy from USA with Italian Passport near Expiration

Traveling to Italy from the US with an Italian passport that will have less than 3 months left before expiration upon arrival in Italy and will also have a valid US Green Card with no expiration impending. I will return to US before six weeks before Italian Passport Expires.

a) will I have issues with departure from the US and entry into Italy ?

b) will I have issues with departure from Italy and re-entry into US ?

…just trying to figure out whether it is worth trying to renew passport before I leave for Italy

Thanks Rosa