I am a Singaporean, now in China, can I apply for Z visa in PRC?

Magdalene, you can try to change the entry permit you hold now to a work Z type at the exit and entry administration of the local PSB in PRC. But I cannot assure it will succeed in the end.
If you don’t have HK residence permit in HK, it’s not easy to get it from there.
So if it cannot be changed within mainland PRC, you are advised to go back and apply for it in your home country.