“Are you planning on asking her out?”
Your friend seems to be attracted to his co-worker. You want to find out what he's going to do about it. You ask this.
Are you planning on asking her out?
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When you are "planning on" doing something, it means that you intend to do it. You want to do it. But it doesn't necessarily mean that you have a strong plan for getting it done. For example, you can say:
I'm planning on throwing a big party for Kevin's 30th birthday in November.
If you say this in May, it doesn't mean that you've planned out a party. It just means that you think you're going to do it.
To "ask someone out" means to invite them to go on a date with you.