Oatmeal that has been processed in a facility with other foods can sometimes contain trace amounts of gluten but usually the trace amounts of gluten are not enough to cause any problems with some people who have gluten health issues.
If you have a gluten intolerance then you should be able to eat some oatmeal without any issues.
Pure oats and pure oatmeal that has not been processed does not contain any gluten so the oatmeal itself has no gluten but gluten can be transferred to the oatmeal when it's processed on and in the machines in the processing facility.
But oatmeal is gluten free itself.
Oatmeal is usually processed in the same facilities that other gluten containing grains are processed in.
Those gluten containing grains are those such as wheat, rye, and barley.