The thing about colonization is that if you think about it enough, the process by which it happens is pretty unlikely. There are far more countries that did not partake in colonization than there were countries which did.

But I think I understand where this question is coming from: Atlantic-Facing Europe and Mediterranean Europe share much of the same social and cultural background. Many great of the "Colonizing Monarchies" of Europe had been "Mediterranean Monarchies," until they turned 'round to face the opposite direction.

I offered an answer to very similar question a long while back, and I'll repeat some parts here to offer some color as to why Italian governments were disinterested in colonization:

Regarding Italian states, apart from the lack of Atlantic ports (which meant being at the total mercy of sometimes hostile Iberian powers to cross into the Atlantic; recall that much of the early colonization period coincides with the Italian Wars, through which Spain seized both the Duchy of Milan and Kingdom of Naples and became hegemon in Italy) the Italian states did not have the institutional apparatus to pursue a colonization policy.

Even as the city-basted "Communal Governments" of the Middle Ages gave way to the dynastic "Signorie" of the Renaissance, the Italian political system was maniacally (and probably detrimentally) focused on balance of power. The very process of state-building in Italy saw cities and towns retaining much of their delicate council-and-executive systems even when falling under the yolk of a great dynasty like the Visconti/Sforza or Medici, or even when falling under the rule of one of the great Republics like Venice or Genoa. While in the Renaissance submission was increasingly formalized by explicit treaties, effective control by the “dominant” power was nonetheless most effectively expressed either by filling the local council with sycophants or imposing the appointment of a sympathetic executive, rather than exclusively leaning on declarations of submission. So while decrees by the Milanese Sforza or Venetian Minor Consiglio carried the weight of law, the effective obedience of these communities could depend on a variety of factors. It is telling that these legal constructs would never even be abridged or replaced until the dawn of the industrial era: an unusual consequence of Venice's surrender to Napoleon was that the cities of the Venetian mainland considered themselves released of their bonds to Venice, and some insisted on negotiating a separate peace. Thus Italian political systems were very good at fostering enfranchisement, trade, and balance of power, but were unwieldy and laborious mechanisms unable to mobilize resources for grand expeditions, colonial or otherwise (Italian military performance against other European states would prove as much). Compare that to the hypercompetitive monarchies of Europe!

But lack of resources this is not entirely unique to Italy: the monarchs of a multitude of European states had not yet completed the consolidation process when they began colonizing. The difference would lie in the immediate need as to how those resources needed to be spent. The Italians were almost continuously at war between 1494 (two years after Columbus' voyage) and 1559; and although France and Spain were habitual participants in these conflicts, understandably it was easier for them to periodically turn away from the chaotic Mediterranean and turn their attention to the Atlantic (especially in the early days when exploration and colonization was more of an afterthought). In this period, the small Italian states were surrounded by war and much too preoccupied with their survival to turn attention and resources to anything else, and thus 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 institutional and social forces which led to colonization!

It's also worth nothing that both the Republic of Venice and Republic of Genoa did develop vast network of outposts across the Mediterranean. At its height, the Republic of Venice alone governed all of Istria and Dalmatia, as well as the islands of Crete, Corfu, Negropont, and Cyprus. These colonies were important stopping points along the trade routes to the great eastern entrepôts and their colonization by Venice and Genoa ran parallel to their rapid economic and social integration. While Italian merchants were indeed present in the early Atlantic trade, the volume of mercantile activity was not sufficient to justify the time and resources to pursue colonies along those trade routes. Even after the slow and steady growth of Atlantic trade, which itself only really impacted the Italians insomuch that it linked up to Indian Ocean trade, the Mediterranean economy didn't stop overnight: people were still moving goods and services from point A to point B. Mediterranean stagnation is better understood as a gradual, century-long loss of capital and trade in favor of the more lucrative Atlantic trade, and the mediterranean trade nonetheless allowed the Italian states to enjoy the third-highest concentration of wealth in Europe until around 1820 (according to Angus Maddison's estimates). So the Italians weren't about to up-end their society for uncertain gains that would nonetheless be at the mercy of the greatest powers of Europe!

Lastly, it's worth noting that Columbus' voyages were themselves partially financed by Genoese bankers, and after King Francis ceded the Duchy of Milan to Charles V of Spain (and Austria) the Republic of Genoa became an important client of the Spanish Empire. As Genoa-Milan-Burgundy axis became and important commercial and military line for the Spanish Empire, Genoese investors and merchants would go on to play an important role in financing Spanish expansion in the Americas. Thus, you could also argue that the Italian elites were indeed involved in colonization on the personal level, just not at the state level.

As for the Ottoman Empire, I'll admit I don't know all that much but I'd point out that they did extensively expand across the Middle East, the Balkans, and North Africa. It would seem that institutionally and socially, the Ottomans preferred to expand their existing borders, rather than cross the ocean.