I only had one cat that scratched furniture, and I didn't have a scratching post yet. I got one right away and put it IN THAT SAME SPOT, right in front of the corner that he liked to scratch on (a routine--eat, go through the kitchen door, scratch, go off to wherever).
So maybe put the scratching post right there, since the rug is in the same spot? And see if she switches?
With mine, the other thing that made it successful is that the sisal-fabric scratching post was much more satisfying than the loosely woven Haitian cotton sofa.