Not a core, but you can make the moss strands latch onto each other by gently rolling the pieces together in your hands. It will be loose. The individual pieces can also be rolled gently by themselves - then you have more, albeit smaller. Either way, they grow s-l-o-w-ly, like, measuring fractions of an inch per year, so you would not be out of place to purchase a new one. Sounds like your goldfish are doing their job, nipping at what the moss collects, so this may be an ongoing thing in the future. At least Marimo moss balls aren't that expensive.