From what I have heard, it is possible to push, pull, stretch, and squeeze the fabric of space. Scientists hope to produce a ship that propells itself by pulling and pushing on space. This ship, relative to everything else, can go to many times the speed of light, while remaining stationary within this tiny spacebubble that it rests in.

So, yes, it is possible to compress the fabric of spacetime. In the process, you will create a gravity feild which will attract things. In fact, the earth itself is compressing space right now using it's mass, therefore producing a gravitational feild.

Its safe to say that, all you need to compress space is mass.