The phrase "update you about" is correct and can be used in written English.
You can use this phrase when you want to give another person information about something, or give them an update on a particular topic. For example: "I just wanted to update you about the progress I've made on the project."
I will update you about these ongoing conversations over the coming weeks.
We are scheduling training sessions, which will begin Monday the 25th, and will be in touch about the upcoming schedule and to continue to update you about our CQ implementation.
It's so ridiculously glorious here on the gallery terrace that it's quite tempting to stretch out and bask in the sunshine, but first we should update you about festival events we've been enjoying so far – and those that we're looking forward to in the next week.
A device that can constantly update you about how sedentary or otherwise your average day is was the inspiration for another piece of wearable tech released this year by Nike.
Busy staff in a hospital are very willing to update you about your loved one, but they shouldn't have to tell the same information over and over again to everyone who wants to know.
Later this week we'll update you about the car's tech and finally a full-review on Friday with some video action — maybe even some fun winter drifting — who knows where the xB will take us this next week.
We will be updating you about the Courseworks Guides issues later today.
I'll continue updating you about Aquaman's fantastic run, so check back soon for more details.
We're also going to be updating you about the new iPhone.
It's almost impossible to get over an ex when Facebook constantly updates you about all the new girls or guys they "befriends".
I wanted to update you on our previous statement about RealMedia deprecation.
