I tried googling this but the only thing that showed up was about the Ottomans specifically (who would be the last people I'd think would colonize). But there were lots of other Muslim Kingdoms/Sultanate who were further west then the Ottomans, and surely Morroco and the Berbers who are in consistent contact with the Europeans in Iberia would have come to the conclusion of "New world make Europe wealthy. We should new world so new world make us wealthy too!"
are you asking specifically about the Americas? Because there were Islamic colonies in other parts of the world.
Why do the Muslims in your question speak like they are developmentally challenged? It makes it difficult to answer your question easily.
I would posit a few answers, all of which are preliminary thoughts:
North African Muslim merchants were at this time involved in quite lucrative trade with sub-Saharan Africa. Until the seventeenth century, at least, they might not have perceived a benefit to switching their trading patterns and/or there might have been institutional and network difficulties in making such a change.
At least initially, because Muslim merchants dominated land-based trade routes to East and South Asia, and profited from their position as middlemen between Europeans and Asians further east, they had little incentive to develop large scale maritime routes in the Atlantic. (Of course, Muslims also dominated large-scale Indian Ocean trade routes, and I'm not sure how convincing this point is).
The "caravel technology gap" might matter here. In the Mediterranean, galleys (which are not long-distance ships but are quite maneuverable) predominated well into the sixteenth century, whereas Atlantic-facing states found the caravel more useful. (Note that Atlantic-facing Senegambian societies that might be characterized loosely as 'Muslim' did not generally possess either technology nor cultures around long-distance maritime routes.
Aside from Morocco, most of the Muslim societies anywhere close to the Atlantic in North Africa were politically vassal states of the Ottoman Empire, which meant that their attention was oriented eastward.
Spain and Portugal could block Mediterranean Muslim societies at the straits of Gibraltar quite easily.
What led Columbus to discover the Americas was that after the Spanish Inquisition and Spain drove the Moors out of the Iberian Peninsula, the Ottoman Empire (allied with the Moors) decided to not to let Spain trade along the Silk Road as the Ottomans controlled it (except the Saffavid Empire controls a bit of it). Without the traditional trade rout to China, Columbus wanted to go over seas to find a new trade route. Therefore, they didn't need the extra trade route because they were plenty good with the one they'd been using since the Silk Road was created.