If the room is carpeted, you may (note: "may") be able to hide the cord by pushing it down between the edge of the carpet and the baseboard. If the trim carpenter was a professional and knew the room would be carpeted, he "may" have left the bottom of the baseboard, 1/4" or so, above the slab so as to allow the carpet edge, after it has passed over the nail strip, to be pushed into the small gap. If you try this, for heaven's sake, use only a wooden tool, perhaps the end if a paint stirrer, and be careful to not puncture the insulation on the nail strip which holds the carpet in place.
Having said this, you would be wise to hire an electrician to install a new outlet. The best ones use a directional drill and can bore holes through any wall studs between the two boxes, using only the hole in the sheetrock for the old outlet and the one for the new outlet.
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