Let's think of Saturn, because of its density. Can there be a place near the center of the planet where the gravity upwards is more than towards the center, and with an atmosphere that is more suitable for life. Yes, I am calling the hollow Earth extreme, but is it that for a giant gas planet too. Can it be possible?
Newton's shell theorem proves that inside a gas giant, any layers that are further than you from the centre have a zero gravitational effect on you. So if you are inside a gas giant (and by some magic not dead) the only gravity comes from the layers that are closer to the centre. So the gravitational pull is always down.
If fact, the pressure increases as you go down, as the weight of the layers above you causes pressure (just as the the Earth's air is more dense the lower you go). Since the gas is under extreme pressure, it would fill up any gap that formed, (just like the air fills a vacuum on Earth) In a gas giant the pressures are extreme, there is certainly no way that a hole or cavity could ever form.