Inside nanobubbles would probably be "a high-pressure gas". Whether it be an inert gas or vaporized surrounding liquid depends on the temperature, pressure, components, and many other experimental variables.

Regarding theory on nanobubbles, and starting from a classical, macro-scale standpoint, the [Laplace pressure][1] describes the pressure inside a bubble due to surface tension on the curved vapor-liquid surface. The pressure will be necessarily higher inside the bubble in order that it doesn't collapse.

For nanobubbles, things get more interesting. The surface tension is not constant with curvature and at the extreme curvatures necessary for nanobubbles this will change things. A first-order approximation to surface tension corrections is the [Tolman length][2]. Also, at the high pressures involved gases would not be ideal, so some equation of state is likely necessary.


  [1]: https://en.wikipedia.org/wiki/Laplace_pressure
  [2]: https://en.wikipedia.org/wiki/Tolman_length