I mean besides Mussolini's attempt to build one.
In what sense?
Italy is an old nation, but a young country. After Napoleon, societal pressures within Italy pushed the rulers of the Kingdom of Piedmont-Sardinia to fight a series of wars between 1848 and 1870 against the Austrian Empire, the Kingdom of the Two Sicilies, and the Papal States in order to unite the country. I gave some context here.
The nascent Kingdom of Italy was much too preoccupied with the process of setting up the institutional infrastructure of the state to invest any significant energy in colonization. Besides, by the time the Italian unification process was complete much of Africa and the Americas had already been partitioned. But there were nonetheless some efforts taken to found colonies, and the Italian political establishment yearned for the political prestige and international recognition that colonial possessions would afford. Early sights were set on the nearby North African land of Tunisia, however tensions with France stalled any action. The new Italian governments' first foray into colonialism dates to the 1860s, when Italian missionaries and merchants began appearing in Eritrea, which at the time was a coastal region of Abyssinia (an independent state located on the horn of Africa more or less corresponding to modern-day Ethiopia). Taking advantage of a inattentive Sultanate of Egypt (at the time transitioning from Ottoman to British protection) which disputed the coast with Ethiopia, the Italian government oversaw the seizure of strategic ports on the Red Sea. Continued Italian encroachment inland would eventually spark an open conflict with Abyssinia, which would only be resolved with the signing of a peace treaty in 1896, recognizing Italian control over Eritrea. Under Fascist rule, war against Abyssinia would resume in the 1930s to subdue the whole of the horn of Africa.
Italian authorities also stipulated a number of protectorate agreements with local sultans farther south along the Horn of Africa, in Somalia. This would lay the foundation for a military and administrative presence, as well as the construction of colonial communities and settlements. The various Somalian protectorates and settlements would be merged in a single administrative unit in 1908, however Italian control was never really consecrated beyond coastal cities.
Italy also outright seized provinces from weaker powers. In 1911, Italy invaded the North African regions of Tripolitania and Cirenaica, which today are part of Libya but at the time were semi-autonomous sultanates protected by the Ottoman Empire. In order to open up a second front against the Ottomans, Italy also seized the islands of the Dodecanese, off the southwestern coast of Anatolia. The Italian state would then have to deal with Libyan guerrillas (while never really projecting power in the country's interior) as well as a hazy legal status around the Dodecanese which would only be resolved in 1920.
Lastly and perhaps less significantly, in 1901 the Italian government stipulated a small concession in the Chinese city of Tientsin along with several other European powers.
Prior to unification, Italian states simply did not have the institutional apparatus to pursue a colonization policy. Besides, individual bankers, merchants, and navigators from places like Genoa, Milan, and Venice certainly participated in the colonization process as either private citizens or employees of other governments. It's worth noting that Columbus' first voyage was partially financed by Genoese bankers, and after King Francis ceded the Duchy of Milan to Charles V of Spain (and Austria) Columbus' country of origin, the Republic of Genoa, became an important client of the Spanish Empire. The Genoa-Milan-Burgundy axis became and important supply line to the Spanish Netherlands, while Genoese investors and merchants played an important role in financing Spanish expansion in the Americas. So you could also argue that the Italian elites were involved in the affairs of Europe's great powers, and by extension colonization, on the personal level but not at the state level.
The Italian governments themselves just didn't have the capacity to have any sort of atlantic policy, nor did they really have the need or desire to develop one. Besides, the Italian states were almost continuously at war between 1494 and 1559. While other European states like France and Spain almost always took sides and also participated in these conflicts, their Atlantic-facing ports allowed them to easily develop distinct mediterranean and atlantic policies while also keeping an eye on their various European wars.
So the small Italian states were literally surrounded by war and much too preoccupied with their own survival to turn attention or resources to anything else. This means they missed out on the entire early colonization process. In fact, through this lens you could very well argue that French and Spanish involvement in Italy is the other side of the same coin as colonization!
It's also worth pointing out that Italian states developed different kinds of colonies. The Republic of Venice had an extensive colonial empire in the eastern Mediterranean, encompassing all of Istria and Dalmatia as well as the islands of Crete, Corfu, Negropont, and Cyprus. However, these colonies were used as stopping points along the trade routes to Alexandria and Istanbul, or as bases from which to project power in the Adriatic and Aegean seas; whereas the Atlantic Ocean was not at all up the alley of the Venetians and their trade routes. Directing resources across the Atlantic would have comported a massive re-alignment of the Venetian state and economy. It just didn't make sense: although the Atlantic trade was certainly an economic boon for Western Europe, the Mediterranean economy didn't stop overnight, and people were still moving goods and services from point A to point B.