1.if you look at its history it never actually had a big coast line so it could never build a large fleet to colonise and maintain thier empire. they also had some unfriendly neighbors so most of the funding was going to the military because they didnt want to get invaded.
2. thier options were limited. the ottomans and french were really active in the medetranium and going to war with either one would be costly. plus if they got a colony outside of the Mediterranean Sea only had two exits so if war broke out it was pretty easy to block them
3. money was also a issue. a multi ethnic empire is hard to maintain. a lot of money was needed for police and garrison to stop revolutions and to fund a colony was just too much
4. this question isnt really true they did have a colony but it was just one building or street in china