While being one of the few who likes 1998's Godzilla and disagreeing with some of the statements made on that movie in this thread, I can see a profitable Godzilla movie being made with, at the very least $50 million. But I still don't think that will do it. It would almost need to have a $90-$100 million budget to bring in one or two familiar actors to make the movie "legit" in the studio's eyes and to do massive CGI work with the monsters and destruction scenes. Travel expenses included.
The 1998 Godzilla movie was profitable. Sequels were set despite that it didn't produce the income Sony had hoped for, but it was enough for them to be thinking sequels. The reason why no sequels were made? Parts of the fandom cried foul and added to this ridiculous campaign that the 1998 film was the worst ever made when more than have of the actual Japanese franchise wreaking of something foul. I know most don't agree with me on this but that's my two cents.