There are a few ways to ask this question.
Most of the time you would say, “How are you?”. If we are good friends, the more common informal question would be “What’s up?” Or “What’s going on?”
“I’ll catch up with you” does make sense, but it is something that a boss might say to you. Such as if you ask them a question and they can’t respond to you right away.
Something you might say as you are leaving would be “I’ll catch up with you later” which would mean you want to talk to someone but you don't have time at the moment.
If you are younger, the slang phrase would be “What’s the tea?” Which means “What is the gossip / news?” If you ask that to an older person, they might not know what you are asking them.