So far in the Tournament we've seen some of the Jounins such as Shino's sensei and Shikamaru's sensei (I forgot their names), but Gai hasn't been shown yet even though Neji made the finals. We know that Kakashi was off training Sasuke so it's logical to think that he's away with him somewhere (late...). We've even seen Baki at the arena but then we know that he's involved in the Sound / Wind plot.

I get the idea that Gai doesn't give a crap about Neji and he was off tending to Lee in the hospital or something during the past month. He wasn't even shown with him during training (only Tenten was) while the other team jounins helped their student/soldier.