They have the ability but I don’t think they are doing secret programs. They aren’t set up for that, and they kinda suck at keeping secrets.
DIA, DARPA, those kinds of entities would be able to (and have done so).
https://www.amazon.com/Intercept-UFO-Renato-Vesco/dp/B0006WI572
There are those — including some former astronauts — who believe that NASA has kept quite a few secrets about UFO sightings and alien contact.