According to the Defiant-Class MSD, the ship's impulse engines take up the whole aft section of the ship:
However, on the ship itself the impulse engines are off to the side, just next to the warp nacelles:
Looking at the ship that way, there is far more internal space available.

However, on the ship itself the impulse engines are off to the side, just next to the warp nacelles:

Looking at the ship that way, there is far more internal space available.