Perhaps the most accurate answer to this is that we simply don’t know for sure at the moment! It is suggested, however, that something does exist as a core at the centres of gaseous worlds.
These cores are often described as rocky by astronomers. However, this description of them, especially in the case of the gas giant Jupiter, is a little misleading especially as its core is made of liquid compounds, including molten heavy metals such as hydrogen surrounded by ice. Also in Jupiter’s case, the closer you move to the centre, the higher the pressure and temperature gets. What this essentially means is that rather than being thoroughly solid, this core is most likely to be quite slushy with a consistency of both solid and liquid.
A theory surrounding the formation of giant planets of gas suggests that there is almost definitely a core. This idea is called the bottom-up theory or core-accretion model. Here, a ten Earth-mass protoplanet formed, which quickly swept up gas from the primordial disk that formed our Solar System to develop a massive atmosphere around it and become the gas giant Jupiter. The general theory is that the rocky core would have had to have formed very early in the history of the Solar System in order to capture such a high percentage of gases.
Image courtesy of the Lunar and Planetary Institute