It is unlikely that Saturn’s ring system will ever form one large moon. Saturn has an extensive ring system, with more than ten different sections to it. However, the ring system is extremely thin, just ten metres (30 feet) thick on average, and is made up of mostly very small ice particles, so even if a moon was made from all the ring particles it would only be a few hundred kilometres across.
There are many moonlets located within the ring system that are proposed to have formed from material in the rings, but these are usually from several hundred metres to a few kilometres in diameter, much smaller than the objects we usually call moons.
Some of the rings are known to be actively replenished by mechanisms such as the moon Enceladus shooting ice from cryovolcanoes into the ring system. This type of process would make it difficult for particles in that ring to coalesce together to form another moon, or even a moonlet.
There is evidence for other moons of the Solar System to have been formed in this way, however. For example, our own Moon is thought to have formed from the leftover debris after a planet-sized body crashed into Earth early in its history.