It could be many things besides the strut itself. A lot of times the culprit is a bushing somewhere in the suspension (like for the anti-sway bar or the links that connect the sway bar to the suspension). Look for any contact or connection points in the front suspension (could be mounting areas for the springs as well). If any look dried out and or rusted, try spraying some WD-40 and see if it helps. You will have to use a grease or silicone lube for long term solution, but to just find the source, the WD-40 is good enough.

Also look for pivot points in the A-arms, etc. Every joint in the suspension is a suspect! The actual shaft of the strut itself rarely causes noise unless it is totally fried, and I don't think that this is the case here. Likely a rubber bushing that has gotten dirt between rubber and metal or the rubber is brittle and causing the noise from rubbing on metal. Good luck!