what type of duct?
supply duct? return duct?
flex? sheet metal
or panned ( wall cavity used as duct)??

answer is don't know with so little
description. post the construction pic.

best of luck.

Hi.
How about spanning the studs with a real nice looking piece of wood that will go good with your decor then mount the towel ring on the wood.
Woodbutcher

Hi sorry thought I specified. Hot air duct made of ovular sheet metal. I'll post the construction pic

here is the picture

Oval is usually exhaust venting and if so, it's incorrectly strapped.
Select another location.

could be but not always.

hang on stud to right.
putting a hole in the duct won't support the
towel rack & will be a forever leakage
site on the duct.

best of luck..

Looks like you could go a couple of inches to the left or right of the center of the duct and have clearance for a drywall anchor. Drill a 1/16" hole just through the sheetrock, probe by hand with the bit to see what clearance you have, and put in the anchor...or move it a few inches to a better position. The sryle of anchor in the link below is pretty solid and doesn't require much depth.

Here is a link that might be useful: Anchor

From my experience I've found drywall anchors don't hold up over time when they're the only thing holding up towels bars/rings. The anchor eventually becomes loose from the constant use of the towel.

I'd look for another spot to mount the towel holder or buy a decorative towel stand/holder that sits on the counter.

annz-
You're right that many drywall anchors fail, particularly those crappy, expanding plastic ones. The type I showed in my link have secured towel racks and TP holders without a problem for the last 10 years in my house. Another secure mounting technique is a molly bolt. However, nothing is as good as a stud.