Help needed with Rattle in my floorstanding speakers.

I tighten my drivers yearly, mine have removable backs and all drivers are fastened from within.

Otherwise, you will need to remove them, I would do them all at once, perhaps adding bullet connectors in-line for easier access.

If insulation, you can remove existing, partially or all, and replace with polyfill, I got mine from Walmart, one small bag expands to a heck of a lot.

Once, when a woofer was facing down (speakers on 8" high open base, a buzz turned out to be a staple that had fallen out and landed on the back of the cone. i.e. you never know, just be thourough.

probably a wire routed too close to a bare wall or a driver magnet.  take each upper driver out.  As you pull it out note the wire routing and look for the source of the rattle.

Jerry

I really think it is one of the scenarios mentioned above regarding loose wire or so. I will remove the drivers and check this weekend. 

If the drivers are tight, and it's not them, the most likely culprit is a loose wire.  After that a crossover board and lastly cabinet component.

Without knowing what speaker it is, I would suggest removing the grilles (if any) before going further. Some grille frames are steel or aluminum and may very well cause an audible rattle if not secured against the speaker or if the frame came loose at a joint.