That is a very good question. And the answer is yes. A gas can be more dense than a liquid. But the conditions for this to be met are pretty difficult to come by. The density of a gas is dependent upon the pressure and the temperature that it is under.

The density of a gas is directly proportional to the pressure and indirectly proportional to the temperature. This means that if the pressure increases, the density will increase and if the temperature decreases the density will increase.

The density of a liquid on the other hand is always constant. Which is measure by the mass of the liquid divided by the volume. So if you can imagine a place that is really cold and under a lot of pressure, for instance, in space in a black hole or at the bottom of the ocean, you could make a gas more dense than liquid. I hope this helps and keep asking those questions!