Given how eager Legendary Pictures in particular has been to develop franchises, it should be a no-brainer for all involved to start working on ideas for another movie, especially since Legendary and Warner Bros have been considering the prospect for a while now.
Godzilla is now stomping towards an estimated $196.2 million worldwide in its first weekend. Director Gareth Edwards has hinted in the past that he has ideas for a potential sequel, but has kept further details under his hat, preferring to let his work do the talking. Now we're certain he'll be besieged with calls officially asking him to take on on the new film, though he may still choose to do what he did with Monsters (2010), and let someone else handle any sequels.
Expect to hear more on Godzilla 2 (or whatever the title may be) soon. As always, watch this space.