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We don't really know. Personally, I would have to assume there is some kind of solid mass in the center just from the pressure forcing shit together. If gasses are compressed enough, they become solid. But if there is too much pressure, it can become liquid (or, well, fluid?) again; like stars.
But, also, the pressure is so much, you'd probably float before you were crushed. I can't imagine that the massive pressure doesn't also come with massive density.
Also i would assume there's solid stuff like meteors at the center anyway.
You would keep falling until you hit the core, whether it was solid or liquid.
The important thing it that it wouldn't matter because you would implode from the pressure before you ever even got close.
You could theoretically stand on the core of a gas giant if you were superman. For a regular human, entering a gas giant would be like falling into an ever increasing atmosphere, even if you decended slowly, the pressure and turbulence would basically crush you and tear you apart into you constituent atoms long before you reached any core. The atmoshpere on earth is like the skin of an apple, just a thin lil coating on there. The atmoshphere of a gas giant is like the meat of a peach, big, thick and juicy. Reaching the core of a gas giant would be akin to trying to reach the core of our planet, except you don't have a cold hard crust to stand on, it's just atmo, thicker atmo with pressures exceeding the marianas trench and crazy winds and chemicals, then it gets hot af and even more pressure atmo, etc. depending on the planet there's winds in excess of 1000mph, maybe electrified, maybe containing molten metals, etc. there's usually a liquid bit in there on the core too. This dude does simulations of different gas giants. Here's Uranus