Depends on several things, but the three big ones are tankmates, filtration, and size of course.
Hypothetically speaking, if you had a large filtration system with lots of biological filtration, and the gourami was the only fish, and you were doing regular water changes, you would be fine in about a 180-220 minimum.
However, I'm sure you want other fish, so I would recommend at least a 300+, with regular water changes and tons of bio-filtration. Giant Gouramis are pretty dirty fish from what I know