The answer at this point in time is no, but it is possible to gain permanent residency by demonstrating a certain annual income and, even better, a large investment in properties.
How Can You Get Italian Residency & Citizenship by Investment?
In 2017 Italy introduced a new programme namely “Investor Visa for Italy” where the minimum requirement can be either:
At this time, Italy does not allow visas for pure real estate investment.
Among other requirements, you need to be a no-EU citizen and have no criminal record.
In order to obtain your investor visa you first need a certificate of no impediment (Nulla Osta). Once you obtain the Nulla Osta, you can go to the Italian representation in your country of residence where you can apply for a two-years investor visa. This visa is revewable for further 3 years if you mantain your donation or investment.
After five years of residence, you can become permanent resident in Italy, and you can become an Italian citizen after ten years of residence. Here is how investors acquire Italian citizenship.