Logically the universe is expanding into nothing – but science does not like ‘nothing’ (no thermal energy, no light, no radiation of any kind). Scientists would argue that the ‘nothing’ does not exist (and cannot exist).
Since our universe is expanding at the speed of light (in all directions), it is impossible to determine what it is expanding into. If you could travel faster than light and reach beyond the edge of our universe – you would still be part of our expanding universe (and could never reach the ‘nothing’).
What would be interesting is if another expanding universe were to encroach on our universe (like two galaxies colliding).