One of my colleagues told me that one of his family members is having health problems. The last few days he has been very sad, so I wanted to ask him if everything is okay or not. In the country where I am from it is okay to discuss any questions between colleagues (even something so personal), but I'm not sure if it is okay or not to ask such personal questions here in North America. I want to support him, but I don't want to be rude. Is it okay to ask him about his family member's health in this situation?
If he's already told you about the issues then I would say it's okay to inquire but I'd make it clear that you totally understand if he doesn't want to talk about it.
Hi [colleague], I don't want to pry but I wanted to see if you were okay. Not a problem if you'd rather not talk about it but I'm here to listen if you want.
Yes!! don't be invasive but definitely demonstrate that you remember it and you care about it! Sometimes just a colleague demonstrating to care about you really makes the day!
Use something like:
How that situation about your relative that you told me is going?
If you feel you can also add an :
in case you need something just ask...