The center of the ankle shows the ankle mortise view on radiograph, ie, X Ray. You may visualize a defect in the talar dome or damage to the talus or more proximally the tibia. You may check for any bone spurs. It's a good idea to start with plain film X Rays, rule out any kind of bony process that may cause the "click". If there's a bone spur present, resection of the protrusion may make the click go away, providing more comfort.
Evaluate the long extensor tendons over the dorsum of the ankle. Are they taut? Do they "click" upon ambulation? Something like this may need to be accommodated by orthotics, depending upon the foot type. Surgical corrections may elongate the tendons, if conservative care isn't enough of a correction. If it's a cavus foot type, however, evaluation of the cause of the concern, and surgical corrections and even conservative accommodations can be rather complex.
Does the click occur in a certain shoe type? The shoe laces may be too tight over the dorsum of the foot. Make sure the dorsum of the foot has enough room to function normally.
The achilles tendon may be too taut, evaluate the patient for equinus. If the click happens with a gastroc or gastroc soleus equinus, a heel lift such as a boot with a heel on it, and regular stretching of the achilles tendon, like a runner's stretch, may help quite a bit.