Embossing a model's texture onto its mesh

I've got an .obj file that I've imported into Blender from another application. The imported model includes a complex texture nicely mapped onto it, and it renders nicely. However, I'm planning to 3D print the object, and so I'd like to get some of the detail from the texture onto the model.

I looked around and found the "displace" modifier, which seems like it should maybe be what I need, but I can't figure out a way to tell it to use the texture that the mesh is already using. Instead, it seems like the modifier wants me to create a new texture?