Nope. Closest mulberry is at least a couple hundred feet away. Not that any tree roots can't be destructive. Had a large old Maple removed a while back cause it was only a few feet from my garage. Was already f'n up the sidewalk and concrete driveway.
I got a 40ish foot mulberry in the yard next to my shed. Roots have raised its foundation about 10 inches. And they're headed for my house! It gets cut down this winter. Almost sacrilege to cut down any tree here, but it must be done.