According to the early script by Terry Rossio and Ted Elliot, the Gryphon was to appear in Utah first, then destroy it's way to New York and battle Godzilla. The creature comes to Earth in a meteorite, and promptly begins to consume animals, gathering the genetic material from many different fauna to construct a new body for its self, indicating that it may not have been a solid organism, rather a mass of organic material like the Blob. It could attack with claws, teeth, a group of snakes living in it's mouth, and blasts of electricity from it's wings. It could also modify bats to collect animals for it.
According to some sources, Toho's agreement with TriStar expressively forbade them from creating any monsters of their own (although Toho seems to have conceded this in the case of Godzilla: The Series). Toho seems to have told TriStar that if "their" Godzilla was to battle another creature, it had to be a Toho creation. The two monsters Toho offered, Mothra and King Ghidorah, were much too expensive, making Tristar decline. After this, the project was scrapped but the concept art had already been released.